Radicals & Absolute Values - SAT Math
Card 1 of 30
Solve for $x$: $\text{√}x = 5$.
Solve for $x$: $\text{√}x = 5$.
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$x = 25$. Square both sides to eliminate the radical.
$x = 25$. Square both sides to eliminate the radical.
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State the property: $|\text{a}| \times |\text{b}| = ?$
State the property: $|\text{a}| \times |\text{b}| = ?$
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$|\text{a} \times \text{b}|$. Absolute values multiply to give the absolute value of the product.
$|\text{a} \times \text{b}|$. Absolute values multiply to give the absolute value of the product.
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What is the absolute value of 0?
What is the absolute value of 0?
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- Zero has no distance from itself.
- Zero has no distance from itself.
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What is $\text{√}(-9)$?
What is $\text{√}(-9)$?
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Not a real number. Square roots of negative numbers aren't real.
Not a real number. Square roots of negative numbers aren't real.
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Express $\text{√}32$ in simplest radical form.
Express $\text{√}32$ in simplest radical form.
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$4\text{√}2$. Factor out perfect squares: $\sqrt{32} = \sqrt{16 \times 2}$.
$4\text{√}2$. Factor out perfect squares: $\sqrt{32} = \sqrt{16 \times 2}$.
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State the property: $|\text{a}| + |\text{b}| \neq ?$
State the property: $|\text{a}| + |\text{b}| \neq ?$
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$|\text{a} + \text{b}|$. Triangle inequality shows they're not always equal.
$|\text{a} + \text{b}|$. Triangle inequality shows they're not always equal.
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What is the result of $|\text{-25}|$?
What is the result of $|\text{-25}|$?
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- Absolute value removes the negative sign.
- Absolute value removes the negative sign.
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Solve for $x$: $|\text{2x} - 3| = 5$.
Solve for $x$: $|\text{2x} - 3| = 5$.
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$x = 4$ or $x = -1$. Distance equals 5, so $2x - 3 = \pm 5$.
$x = 4$ or $x = -1$. Distance equals 5, so $2x - 3 = \pm 5$.
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What is $\text{√}64$?
What is $\text{√}64$?
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- Since $8 \times 8 = 64$.
- Since $8 \times 8 = 64$.
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Solve for $x$: $|\text{x} + 5| = 8$.
Solve for $x$: $|\text{x} + 5| = 8$.
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$x = 3$ or $x = -13$. Distance from -5 equals 8, so $x + 5 = \pm 8$.
$x = 3$ or $x = -13$. Distance from -5 equals 8, so $x + 5 = \pm 8$.
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Simplify $\text{√}0.25$.
Simplify $\text{√}0.25$.
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0.5. Since $0.5 \times 0.5 = 0.25$.
0.5. Since $0.5 \times 0.5 = 0.25$.
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What is the absolute value of $|\text{3} - 7|$?
What is the absolute value of $|\text{3} - 7|$?
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- Calculate $3 - 7 = -4$, then take absolute value.
- Calculate $3 - 7 = -4$, then take absolute value.
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What is the square of $\text{√}3$?
What is the square of $\text{√}3$?
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- The square of a square root equals the radicand.
- The square of a square root equals the radicand.
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Simplify $\text{√}8 + \text{√}18$.
Simplify $\text{√}8 + \text{√}18$.
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$2\text{√}2 + 3\text{√}2 = 5\text{√}2$. Simplify each radical first: $\sqrt{8} = 2\sqrt{2}$, $\sqrt{18} = 3\sqrt{2}$.
$2\text{√}2 + 3\text{√}2 = 5\text{√}2$. Simplify each radical first: $\sqrt{8} = 2\sqrt{2}$, $\sqrt{18} = 3\sqrt{2}$.
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Simplify $\text{√}12 - \text{√}3$.
Simplify $\text{√}12 - \text{√}3$.
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$3\text{√}3 - \text{√}3 = 2\text{√}3$. Simplify radicals first: $\sqrt{12} = 2\sqrt{3}$.
$3\text{√}3 - \text{√}3 = 2\text{√}3$. Simplify radicals first: $\sqrt{12} = 2\sqrt{3}$.
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Simplify $\text{√}72$.
Simplify $\text{√}72$.
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$6\text{√}2$. Factor out perfect squares: $\sqrt{72} = \sqrt{36 \times 2}$.
$6\text{√}2$. Factor out perfect squares: $\sqrt{72} = \sqrt{36 \times 2}$.
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Simplify $\frac{\text{√}45}{\text{√}5}$.
Simplify $\frac{\text{√}45}{\text{√}5}$.
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$\text{√}9 = 3$. Divide radicals: $\frac{\sqrt{45}}{\sqrt{5}} = \sqrt{\frac{45}{5}} = \sqrt{9}$.
$\text{√}9 = 3$. Divide radicals: $\frac{\sqrt{45}}{\sqrt{5}} = \sqrt{\frac{45}{5}} = \sqrt{9}$.
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Simplify $\text{√}20$.
Simplify $\text{√}20$.
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$2\text{√}5$. Factor out perfect squares: $\sqrt{20} = \sqrt{4 \times 5}$.
$2\text{√}5$. Factor out perfect squares: $\sqrt{20} = \sqrt{4 \times 5}$.
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What is the square root of 49?
What is the square root of 49?
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- Since $7 \times 7 = 49$.
- Since $7 \times 7 = 49$.
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Solve for $x$: $|\text{x} - 4| = 3$.
Solve for $x$: $|\text{x} - 4| = 3$.
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$x = 7$ or $x = 1$. Distance from 4 equals 3, so $x - 4 = \pm 3$.
$x = 7$ or $x = 1$. Distance from 4 equals 3, so $x - 4 = \pm 3$.
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What is the absolute value of $|\text{-7}|$?
What is the absolute value of $|\text{-7}|$?
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- Absolute value makes negative numbers positive.
- Absolute value makes negative numbers positive.
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Simplify $\text{√}27$.
Simplify $\text{√}27$.
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$3\text{√}3$. Factor out perfect squares: $\sqrt{27} = \sqrt{9 \times 3}$.
$3\text{√}3$. Factor out perfect squares: $\sqrt{27} = \sqrt{9 \times 3}$.
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Simplify $\text{√}200$.
Simplify $\text{√}200$.
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$10\text{√}2$. Factor out perfect squares: $\sqrt{200} = \sqrt{100 \times 2}$.
$10\text{√}2$. Factor out perfect squares: $\sqrt{200} = \sqrt{100 \times 2}$.
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Solve for $x$: $|\text{x}| = 12$.
Solve for $x$: $|\text{x}| = 12$.
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$x = 12$ or $x = -12$. Absolute value equation has two solutions: $x = \pm 12$.
$x = 12$ or $x = -12$. Absolute value equation has two solutions: $x = \pm 12$.
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What is the principal square root of 81?
What is the principal square root of 81?
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- Since $9 \times 9 = 81$.
- Since $9 \times 9 = 81$.
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Solve for $x$: $|\text{3x} + 2| = 11$.
Solve for $x$: $|\text{3x} + 2| = 11$.
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$x = 3$ or $x = -\frac{13}{3}$. Distance equals 11, so $3x + 2 = \pm 11$.
$x = 3$ or $x = -\frac{13}{3}$. Distance equals 11, so $3x + 2 = \pm 11$.
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What is the result of $\text{√}1$?
What is the result of $\text{√}1$?
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- Since $1 \times 1 = 1$.
- Since $1 \times 1 = 1$.
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Simplify $\text{√}50$.
Simplify $\text{√}50$.
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$5\text{√}2$. Factor out perfect squares: $\sqrt{50} = \sqrt{25 \times 2}$.
$5\text{√}2$. Factor out perfect squares: $\sqrt{50} = \sqrt{25 \times 2}$.
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Simplify $\frac{\text{√}18}{\text{√}2}$.
Simplify $\frac{\text{√}18}{\text{√}2}$.
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$\text{√}9 = 3$. Simplify by dividing: $\frac{\sqrt{18}}{\sqrt{2}} = \sqrt{\frac{18}{2}} = \sqrt{9}$.
$\text{√}9 = 3$. Simplify by dividing: $\frac{\sqrt{18}}{\sqrt{2}} = \sqrt{\frac{18}{2}} = \sqrt{9}$.
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What is the absolute value of -15?
What is the absolute value of -15?
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- Absolute value makes any number non-negative.
- Absolute value makes any number non-negative.
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