How to subtract square roots - PSAT Math

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Question

Evaluate: $\sqrt{108}$-$\sqrt{81}$

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Answer

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

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Question

$\sqrt{63}$-$\sqrt{28}$

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Answer

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

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Question

Evaluate: $\sqrt{108}$-$\sqrt{81}$

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Answer

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

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Question

$\sqrt{63}$-$\sqrt{28}$

Tap to reveal answer

Answer

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

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Question

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Tap to reveal answer

Answer

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

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Question

$\sqrt{63}$-$\sqrt{28}$

Tap to reveal answer

Answer

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

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Question

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Tap to reveal answer

Answer

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

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Question

$\sqrt{63}$-$\sqrt{28}$

Tap to reveal answer

Answer

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

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Question

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Tap to reveal answer

Answer

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

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Question

$\sqrt{63}$-$\sqrt{28}$

Tap to reveal answer

Answer

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

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Question

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Tap to reveal answer

Answer

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

← Didn't Know|Knew It →

Question

$\sqrt{63}$-$\sqrt{28}$

Tap to reveal answer

Answer

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

← Didn't Know|Knew It →

Question

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Tap to reveal answer

Answer

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

← Didn't Know|Knew It →

Question

$\sqrt{63}$-$\sqrt{28}$

Tap to reveal answer

Answer

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

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Knew It

How to subtract square roots - PSAT Math

Evaluate:

Let us factor 108 and 81

Step one: Find the greatest square factor of each radical For this is , and for it is . Therefore: Step two: Simplify the radicals

Evaluate:

Let us factor 108 and 81

Step one: Find the greatest square factor of each radical For this is , and for it is . Therefore: Step two: Simplify the radicals

Evaluate:

Let us factor 108 and 81

Step one: Find the greatest square factor of each radical For this is , and for it is . Therefore: Step two: Simplify the radicals

Evaluate:

Let us factor 108 and 81

Step one: Find the greatest square factor of each radical For this is , and for it is . Therefore: Step two: Simplify the radicals

Evaluate:

Let us factor 108 and 81

Step one: Find the greatest square factor of each radical For this is , and for it is . Therefore: Step two: Simplify the radicals

Evaluate:

Let us factor 108 and 81

Step one: Find the greatest square factor of each radical For this is , and for it is . Therefore: Step two: Simplify the radicals

Evaluate:

Let us factor 108 and 81

Step one: Find the greatest square factor of each radical For this is , and for it is . Therefore: Step two: Simplify the radicals

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$

Evaluate: $\sqrt{108}$-$\sqrt{81}$

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= $2^2$\times 3\times 9= $2^2$\times $3^2$\times 3$

$81=9\times $9=9^2$$

$$\sqrt{108}$-$\sqrt{81}$=6$\sqrt{3}$-9$

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}$-$\sqrt{28}$=$\sqrt{97}$-$\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}$-$\sqrt{47}$

$3$\sqrt{7}$-2$\sqrt{7}$$

$\sqrt{7}$