SAT Math Flashcards: Radicals And Absolute Values

What this deck covers

This deck focuses on Radicals And Absolute Values, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Simplify $\frac{\text{√}18}{\text{√}2}$.

Answer: $\text{√}9 = 3$. Simplify by dividing: $\frac{\sqrt{18}}{\sqrt{2}} = \sqrt{\frac{18}{2}} = \sqrt{9}$.

Flashcard 2: State the property: $|\text{a}| + |\text{b}| \neq ?$

Answer: $|\text{a} + \text{b}|$. Triangle inequality shows they're not always equal.

Flashcard 3: Simplify $\text{√}12 - \text{√}3$.

Answer: $3\text{√}3 - \text{√}3 = 2\text{√}3$. Simplify radicals first: $\sqrt{12} = 2\sqrt{3}$.

Flashcard 4: Simplify $\text{√}72$.

Answer: $6\text{√}2$. Factor out perfect squares: $\sqrt{72} = \sqrt{36 \times 2}$.

Flashcard 5: What is the principal square root of 81?

Answer:

1. Since $9 \times 9 = 81$.

Flashcard 6: What is the absolute value of 0?

Answer:

1. Zero has no distance from itself.

Flashcard 7: Simplify $\text{√}50$.

Answer: $5\text{√}2$. Factor out perfect squares: $\sqrt{50} = \sqrt{25 \times 2}$.

Flashcard 8: What is the absolute value of -15?

Answer:

1. Absolute value makes any number non-negative.

Flashcard 9: What is the square root of 49?

Answer:

1. Since $7 \times 7 = 49$.

Flashcard 10: Solve for $x$: $|\text{x} + 5| = 8$.

Answer: $x = 3$ or $x = -13$. Distance from -5 equals 8, so $x + 5 = \pm 8$.

Flashcard 11: Simplify: $\text{sqrt}(72)$.

Answer: $6\text{sqrt}(2)$. Factor out perfect squares: $\sqrt{36 \times 2} = 6\sqrt{2}$.

Flashcard 12: State the property: $|\text{a}| \times |\text{b}| = ?$

Answer: $|\text{a} \times \text{b}|$. Absolute values multiply to give the absolute value of the product.

Flashcard 13: Simplify $\frac{\text{√}45}{\text{√}5}$.

Answer: $\text{√}9 = 3$. Divide radicals: $\frac{\sqrt{45}}{\sqrt{5}} = \sqrt{\frac{45}{5}} = \sqrt{9}$.

Flashcard 14: What is the square root of 49?

Answer:

1. Since $7 \times 7 = 49$.

Flashcard 15: Solve for $x$: $|\text{3x} + 2| = 11$.

Answer: $x = 3$ or $x = -\frac{13}{3}$. Distance equals 11, so $3x + 2 = \pm 11$.

Flashcard 16: Solve for $x$: $|\text{3x} + 2| = 11$.

Answer: $x = 3$ or $x = -\frac{13}{3}$. Distance equals 11, so $3x + 2 = \pm 11$.

Flashcard 17: Simplify $\text{√}8 + \text{√}18$.

Answer: $2\text{√}2 + 3\text{√}2 = 5\text{√}2$. Simplify each radical first: $\sqrt{8} = 2\sqrt{2}$, $\sqrt{18} = 3\sqrt{2}$.

Flashcard 18: What is the absolute value of -15?

Answer:

1. Absolute value makes any number non-negative.

Flashcard 19: What is the result of $\text{√}1$?

Answer:

1. Since $1 \times 1 = 1$.

Flashcard 20: Simplify $\text{√}50$.

Answer: $5\text{√}2$. Factor out perfect squares: $\sqrt{50} = \sqrt{25 \times 2}$.

Flashcard 21: Solve for $x$: $\text{√}x = 5$.

Answer: $x = 25$. Square both sides to eliminate the radical.

Flashcard 22: State the property: $|\text{a} \times \text{b}|$.

Answer: $|\text{a} \times \text{b}| = |\text{a}| \times |\text{b}|$. The absolute value of a product equals the product of absolute values.

Flashcard 23: Simplify $\text{√}20$.

Answer: $2\text{√}5$. Factor out perfect squares: $\sqrt{20} = \sqrt{4 \times 5}$.

Flashcard 24: What is the absolute value of $|\text{3} - 7|$?

Answer:

1. Calculate $3 - 7 = -4$, then take absolute value.

Flashcard 25: Express $\text{√}32$ in simplest radical form.

Answer: $4\text{√}2$. Factor out perfect squares: $\sqrt{32} = \sqrt{16 \times 2}$.

Flashcard 26: What is $\text{√}64$?

Answer:

1. Since $8 \times 8 = 64$.

Flashcard 27: What is the result of $|\text{-25}|$?

Answer:

1. Absolute value removes the negative sign.

Flashcard 28: Solve for $x$: $\text{√}x = 5$.

Answer: $x = 25$. Square both sides to eliminate the radical.

Flashcard 29: What is $\text{√}64$?

Answer:

1. Since $8 \times 8 = 64$.

Flashcard 30: Simplify: $\sqrt{48} + \sqrt{12}$.

Answer: $6\sqrt{3}$. Simplify to $4\sqrt{3} + 2\sqrt{3} = 6\sqrt{3}$.

Flashcard 31: What is the absolute value of $|\text{-7}|$?

Answer:

1. Absolute value makes negative numbers positive.

Flashcard 32: Simplify $\frac{\sqrt{18}}{\sqrt{2}}$.

Answer: $\sqrt{9} = 3$. Simplify by dividing: $\frac{\sqrt{18}}{\sqrt{2}} = \sqrt{\frac{18}{2}} = \sqrt{9}$.

Flashcard 33: Solve for $x$: $|\text{x}| = 12$.

Answer: $x = 12$ or $x = -12$. Absolute value equation has two solutions: $x = \pm 12$.

Flashcard 34: What is the square root of 64?

Answer:

1. Since $8^2 = 64$, the principal square root is 8.

Flashcard 35: Solve for $x$: $|\text{x}| = 12$.

Answer: $x = 12$ or $x = -12$. Absolute value equation has two solutions: $x = \pm 12$.

Flashcard 36: Simplify $\text{√}0.25$.

Answer: 0.5. Since $0.5 \times 0.5 = 0.25$.

Flashcard 37: Simplify: $\frac{\sqrt{50}}{\sqrt{2}}$.

Answer: $\sqrt{25} = 5$. This simplifies to $\sqrt{25} = 5$ using the quotient property of radicals.

Flashcard 38: What is the value of $|\text{-7}|$?

Answer:

1. Absolute value gives the distance from zero, always positive.

Flashcard 39: Simplify $\frac{\text{√}45}{\text{√}5}$.

Answer: $\text{√}9 = 3$. Divide radicals: $\frac{\sqrt{45}}{\sqrt{5}} = \sqrt{\frac{45}{5}} = \sqrt{9}$.

Flashcard 40: Solve for $x$: $|\text{x} + 5| = 8$.

Answer: $x = 3$ or $x = -13$. Distance from -5 equals 8, so $x + 5 = \pm 8$.

Flashcard 41: What is the result of $\text{√}1$?

Answer:

1. Since $1 \times 1 = 1$.

Flashcard 42: Simplify $\text{√}72$.

Answer: $6\text{√}2$. Factor out perfect squares: $\sqrt{72} = \sqrt{36 \times 2}$.

Flashcard 43: What is the value of $|-7|$?

Answer:

1. Absolute value gives the distance from zero, always positive.

Flashcard 44: State the property: $|\text{a}| \times |\text{b}| = ?$

Answer: $|\text{a} \times \text{b}|$. Absolute values multiply to give the absolute value of the product.

Flashcard 45: What is the result of $|5 - 9|$?

Answer:

1. Calculate $5 - 9 = -4$, then take absolute value to get 4.

Flashcard 46: Simplify $\text{√}12 - \text{√}3$.

Answer: $3\text{√}3 - \text{√}3 = 2\text{√}3$. Simplify radicals first: $\sqrt{12} = 2\sqrt{3}$.

Flashcard 47: What is $\text{√}(-9)$?

Answer: Not a real number. Square roots of negative numbers aren't real.

Flashcard 48: What is the result of $|5 - 9|$?

Answer:

1. Calculate $5 - 9 = -4$, then take absolute value to get 4.

Flashcard 49: Solve for $x$: $|x - 3| = 5$.

Answer: $x = 8$ or $x = -2$. Distance from 3 equals 5, so $x - 3 = 5$ or $x - 3 = -5$.

Flashcard 50: What is the cube root of 27?

Answer:

1. Since $3^3 = 27$, the cube root is 3.

Flashcard 51: What is the absolute value of $|\text{3} - 7|$?

Answer:

1. Calculate $3 - 7 = -4$, then take absolute value.

Flashcard 52: Simplify $\text{√}200$.

Answer: $10\text{√}2$. Factor out perfect squares: $\sqrt{200} = \sqrt{100 \times 2}$.

Flashcard 53: What is the principal square root of 81?

Answer:

1. Since $9 \times 9 = 81$.

Flashcard 54: Express $\text{√}32$ in simplest radical form.

Answer: $4\text{√}2$. Factor out perfect squares: $\sqrt{32} = \sqrt{16 \times 2}$.

Flashcard 55: Simplify $\text{√}20$.

Answer: $2\text{√}5$. Factor out perfect squares: $\sqrt{20} = \sqrt{4 \times 5}$.

Flashcard 56: Solve for $x$: $|\text{x} - 4| = 3$.

Answer: $x = 7$ or $x = 1$. Distance from 4 equals 3, so $x - 4 = \pm 3$.

Flashcard 57: Solve for $x$: $|x - 3| = 5$.

Answer: $x = 8$ or $x = -2$. Distance from 3 equals 5, so $x - 3 = 5$ or $x - 3 = -5$.

Flashcard 58: Solve for $x$: $|\text{2x} - 3| = 5$.

Answer: $x = 4$ or $x = -1$. Distance equals 5, so $2x - 3 = \pm 5$.

Flashcard 59: Simplify $\text{√}0.25$.

Answer: 0.5. Since $0.5 \times 0.5 = 0.25$.

Flashcard 60: Solve for $x$: $|\text{x} - 4| = 3$.

Answer: $x = 7$ or $x = 1$. Distance from 4 equals 3, so $x - 4 = \pm 3$.

Flashcard 61: State the property: $|\text{a}| + |\text{b}| \neq ?$

Answer: $|\text{a} + \text{b}|$. Triangle inequality shows they're not always equal.

Flashcard 62: Simplify $\text{√}8 + \text{√}18$.

Answer: $2\text{√}2 + 3\text{√}2 = 5\text{√}2$. Simplify each radical first: $\sqrt{8} = 2\sqrt{2}$, $\sqrt{18} = 3\sqrt{2}$.

Flashcard 63: What is the absolute value of 0?

Answer:

1. Zero has no distance from itself.

Flashcard 64: Simplify $\text{√}27$.

Answer: $3\text{√}3$. Factor out perfect squares: $\sqrt{27} = \sqrt{9 \times 3}$.

Flashcard 65: Solve for $x$: $|\text{2x} - 3| = 5$.

Answer: $x = 4$ or $x = -1$. Distance equals 5, so $2x - 3 = \pm 5$.

Flashcard 66: What is the absolute value of $|\text{-7}|$?

Answer:

1. Absolute value makes negative numbers positive.

Flashcard 67: Simplify: $\frac{\sqrt{50}}{\sqrt{2}}$.

Answer: $\sqrt{25} = 5$. This simplifies to $\sqrt{25} = 5$ using the quotient property of radicals.

Flashcard 68: Simplify: $\sqrt{48} + \sqrt{12}$

Answer: $6\sqrt{3}$. Simplify to $4\sqrt{3} + 2\sqrt{3} = 6\sqrt{3}$

Flashcard 69: What is the result of $|\text{-25}|$?

Answer:

1. Absolute value removes the negative sign.

Flashcard 70: What is $\text{√}(-9)$?

Answer: Not a real number. Square roots of negative numbers aren't real.

Flashcard 71: What is the square of $\text{√}3$?

Answer:

1. The square of a square root equals the radicand.

Flashcard 72: Simplify $\text{√}200$.

Answer: $10\text{√}2$. Factor out perfect squares: $\sqrt{200} = \sqrt{100 \times 2}$.