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Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume
z is positive.

5sqrt(14z^(2))*4sqrt(21z^(3))=

Simplify. $\newline$ Multiply and remove all perfect squares from inside the square roots. Assume $\newline$ $z$ is positive. $\newline$ $5\sqrt{14z^{2}} \cdot 4\sqrt{21z^{3}} =$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Multiply and remove all perfect squares from inside the square roots. Assume

\newline

z

is positive.

\newline

5\sqrt{14z^{2}} \cdot 4\sqrt{21z^{3}} =

Write expression: Write down the expression to be simplified. $\newline$ We have the expression $5\sqrt{14z^{2}} \cdot 4\sqrt{21z^{3}}$ .
Multiply coefficients: Multiply the coefficients (numbers outside the square roots) together. $5 \times 4 = 20$
Multiply radicands: Multiply the radicands (expressions inside the square roots) together. $\sqrt{14z^{2}} \times \sqrt{21z^{3}} = \sqrt{14 \times 21 \times z^{2} \times z^{3}}$
Simplify multiplication: Simplify the multiplication inside the square root. $\newline$ $14 \times 21 = 294$ $\newline$ $z^{2} \times z^{3} = z^{2+3} = z^{5}$ $\newline$ So, $\sqrt{14 \times 21 \times z^{2} \times z^{3}} = \sqrt{294 \times z^{5}}$
Factor out perfect squares: Factor out perfect squares from the radicand. $\newline$ $294$ can be factored into $2 \times 3 \times 7 \times 7$ , and $z^{5}$ can be written as $z^{4} \times z$ . $\newline$ So, $\sqrt{294 \times z^{5}} = \sqrt{2 \times 3 \times 7 \times 7 \times z^{4} \times z}$
Take out perfect squares: Take out the perfect squares from under the square root. $7 \times 7$ is a perfect square, and $z^{4}$ is a perfect square. So, $\sqrt{2 \times 3 \times 7 \times 7 \times z^{4} \times z} = 7z^{2} \times \sqrt{2 \times 3 \times z}$
Simplify expression: Simplify the expression inside the square root. $2 \times 3 = 6$ So, $7z^{2} \times \sqrt{2 \times 3 \times z} = 7z^{2} \times \sqrt{6z}$
Multiply with coefficient: Multiply the result from Step $6$ with the coefficient from Step $2$ . $\newline$ $20 \times 7z^{2} \times \sqrt{6z} = 140z^{2} \times \sqrt{6z}$

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