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Assuming
x and
y are both positive, write the following expression in simplest radical form.

7y^(3)sqrt(36x^(6)y^(5))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $7 y^{3} \sqrt{36 x^{6} y^{5}}$ $\newline$ Answer:

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Simplify radical expressions with root inside the root

Full solution

Q. Assuming

x

and

y

are both positive, write the following expression in simplest radical form.

\newline

7 y^{3} \sqrt{36 x^{6} y^{5}}

\newline

Answer:

Simplify Square Root of $36$ : Simplify the square root of $36$ . $\newline$ The square root of $36$ is $6$ because $6^2 = 36$ .
Simplify Square Root of $x^{6}$ : Simplify the square root of $x^{6}$ . Since $x$ is positive and the exponent $6$ is even, $\sqrt{x^{6}}$ is $x^{6/2} = x^{3}$ .
Simplify Square Root of $y^{5}$ : Simplify the square root of $y^{5}$ . We can split $y^{5}$ into $y^{4}\cdot y^{1}$ . The square root of $y^{4}$ is $y^{\frac{4}{2}} = y^{2}$ , and the square root of $y^{1}$ remains under the radical as $\sqrt{y}$ .
Combine Simplified Parts: Combine the simplified parts outside the radical. $\newline$ We have $7y^{3} \times 6 \times x^{3} \times y^{2}$ from the previous steps. $\newline$ Multiplying these together gives us $42y^{3} \times x^{3} \times y^{2}$ .
Combine Like Terms: Combine the like terms. $\newline$ $y^{3} \times y^{2}$ can be combined by adding the exponents since they have the same base. $\newline$ This gives us $y^{3+2} = y^{5}$ . $\newline$ So, we have $42 \times x^{3} \times y^{5}$ .
Combine Simplified Parts Inside Radical: Combine the simplified parts inside the radical. We are left with $\sqrt{y}$ inside the radical.
Write Final Expression: Write the final expression. $\newline$ The final expression is $42x^{3}y^{5}\sqrt{y}$ .

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