Understanding Square Roots

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Math › Understanding Square Roots

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Simplify the expression. Find the positive solution only.

$\sqrt{50x^3y^4}$

$5xy^2\sqrt{2x}$

$25x^2y^4\sqrt{2x}$

$xy^2\sqrt{50xy^2}$

$5xy\sqrt{2x}$

Explanation

When working in square roots, each component can be treated separately.

$\sqrt{50x^3y^4}=\sqrt{50}\sqrt{x^3}\sqrt{y^4}$

Now, we can simplify each term.

$\sqrt{50}=5\sqrt{2}$

$\sqrt{x^3}=x\sqrt{x}$

$\sqrt{y^4}=y^2$

Combine the simplified terms to find the answer. Anything outside of the square root is combined, while anything under the root is combined under the root.

$(5\sqrt{2})(x\sqrt{x})(y^2)=5xy^2\sqrt{2x}$

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