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

y^(3)sqrt(28x^(4)y^(6))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $y^{3} \sqrt{28 x^{4} y^{6}}$ $\newline$ Answer:

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Simplify the product of two radical expressions having same variable

Full solution

Q. Assuming

x

and

y

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

\newline

y^{3} \sqrt{28 x^{4} y^{6}}

\newline

Answer:

Express in Exponential Form: First, let's express the square root in exponential form and then combine the exponents. $\newline$ $\sqrt{28x^{4}y^{6}} = (28x^{4}y^{6})^{\frac{1}{2}}$ $\newline$ Now we can multiply the exponents outside the radical by the exponents inside the radical. $\newline$ $y^{3} \cdot (28x^{4}y^{6})^{\frac{1}{2}}$
Simplify Inside the Radical: Next, we need to simplify the expression inside the radical. $\newline$ $28 = 4 \times 7$ , and $4$ is a perfect square, so we can take the square root of $4$ . $\newline$ $(28x^{4}y^{6})^{1/2} = (4 \times 7 \times x^{4} \times y^{6})^{1/2}$ $\newline$ $= (2^2 \times 7 \times x^{4} \times y^{6})^{1/2}$ $\newline$ $= 2 \times \sqrt{7} \times x^{4/2} \times y^{6/2}$ $\newline$ $= 2 \times \sqrt{7} \times x^{2} \times y^{3}$
Combine Terms with Same Base: Now we can combine the terms with the same base using the product rule of exponents. $\newline$ $y^{3} \times 2 \times \sqrt{7} \times x^{2} \times y^{3}$ $\newline$ = $2 \times \sqrt{7} \times x^{2} \times y^{3+3}$ $\newline$ = $2 \times \sqrt{7} \times x^{2} \times y^{6}$
Final Simplification: Finally, we have simplified the expression to its simplest radical form.

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