Factoring and Simplifying Square Roots

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PSAT Math › Factoring and Simplifying Square Roots

Questions 1 - 10

Simplify. Assume all integers are positive real numbers.

$\sqrt[3]{24x^{16}y^{12}}$

$2x^{5}y^{4}\sqrt[3]{3x}$

$8x^{16}y^{12}$

$2x^{8}y^{4}\sqrt[3]{3x^{2}}$

$2x^{2}y^{3}\sqrt[3]{3xy}$

$2x^{5}y^{4}$

Explanation

$\sqrt[3]{24x^{16}y^{12}}$

Index of means the cube root of Radican $24x^{16}y^{12}$

Find a perfect cube in $\rightarrow$ $\sqrt[3]{8\cdot 3}$

Simplify the perfect cube, giving you $2\sqrt[3]{3}$ .

Take your exponents on both variables and determine the number of times our index will evenly go into both.

$x\rightarrow \frac{16}{3}= 5^{\frac{1}{3}} \rightarrow x^{5}\sqrt[3]{x}$

$y\rightarrow \frac{12}{3}= 4 \rightarrow y^{4}$

The final answer would be

$2x^{5}y^{4}\sqrt[3]{3x}$

Simplify. Assume all integers are positive real numbers.

$\sqrt[3]{24x^{16}y^{12}}$

$2x^{5}y^{4}\sqrt[3]{3x}$

$8x^{16}y^{12}$

$2x^{8}y^{4}\sqrt[3]{3x^{2}}$

$2x^{2}y^{3}\sqrt[3]{3xy}$

$2x^{5}y^{4}$

Explanation

$\sqrt[3]{24x^{16}y^{12}}$

Index of means the cube root of Radican $24x^{16}y^{12}$

Find a perfect cube in $\rightarrow$ $\sqrt[3]{8\cdot 3}$

Simplify the perfect cube, giving you $2\sqrt[3]{3}$ .

Take your exponents on both variables and determine the number of times our index will evenly go into both.

$x\rightarrow \frac{16}{3}= 5^{\frac{1}{3}} \rightarrow x^{5}\sqrt[3]{x}$

$y\rightarrow \frac{12}{3}= 4 \rightarrow y^{4}$

The final answer would be

$2x^{5}y^{4}\sqrt[3]{3x}$

Simplify:

$4\sqrt{27}+16\sqrt{75}+3\sqrt{12}$

$98\sqrt{3}$

$80\sqrt{3}$

$16\sqrt{3}$

$92\sqrt{3}$

$96\sqrt{3}$

Explanation

4√27 + 16√75 +3√12 =

4*(√3)*(√9) + 16*(√3)*(√25) +3*(√3)*(√4) =

4*(√3)*(3) + 16*(√3)*(5) + 3*(√3)*(2) =

12√3 + 80√3 +6√3= 98√3

Simplify:

$4\sqrt{27}+16\sqrt{75}+3\sqrt{12}$

$98\sqrt{3}$

$80\sqrt{3}$

$16\sqrt{3}$

$92\sqrt{3}$

$96\sqrt{3}$

Explanation

4√27 + 16√75 +3√12 =

4*(√3)*(√9) + 16*(√3)*(√25) +3*(√3)*(√4) =

4*(√3)*(3) + 16*(√3)*(5) + 3*(√3)*(2) =

12√3 + 80√3 +6√3= 98√3

Simplify

9 ÷ √3

3√3

not possible

none of these

Explanation

in order to simplify a square root on the bottom, multiply top and bottom by the root

Asatsimplifysquare_root

Simplify

9 ÷ √3

3√3

not possible

none of these

Explanation

in order to simplify a square root on the bottom, multiply top and bottom by the root

Asatsimplifysquare_root

Simplify:

√192

8√2

8√3

4√3

4√2

None of these

Explanation

√192 = √2 X √96

√96 = √2 X √48

√48 = √4 X√12

√12 = √4 X √3

√192 = √(2X2X4X4) X √3

= √4X√4X√4 X √3

= 8√3

Simplify:

√192

8√2

8√3

4√3

4√2

None of these

Explanation

√192 = √2 X √96

√96 = √2 X √48

√48 = √4 X√12

√12 = √4 X √3

√192 = √(2X2X4X4) X √3

= √4X√4X√4 X √3

= 8√3

Simplify the radical:

$\sqrt{320}$

$8\sqrt{5}$

$4\sqrt{20}$

$4\sqrt{5}$

$8\sqrt{20}$

$\sqrt{320}$

Explanation

$\sqrt{320}=\sqrt{2\times 160}=\sqrt{2\times 2\times 80}=2\sqrt{80}=2\sqrt{2\times 40}=2\sqrt{2\times 2\times 20}=2\times 2\times \sqrt{20}=4\sqrt{2\times 10}=4\sqrt{2\times 2\times 5}=4\times 2\times \sqrt{5}=8\sqrt{5}$

Simplify the radical:

$\sqrt{320}$

$8\sqrt{5}$

$4\sqrt{20}$

$4\sqrt{5}$

$8\sqrt{20}$

$\sqrt{320}$

Explanation

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