Chan Lane
02/27/2023 · High School
Simplify: \( \sqrt{48 x^{2} y^{3}} \) \( 4|x y| \sqrt{y} \) \( 4 x y \sqrt{3} \) \( 4 x y \sqrt{3 y} \) \( 4|x y| \sqrt{3 y} \)
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Step-by-step Solution
Calculate or simplify the expression \( \sqrt{48 x^{2} y^{3}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\sqrt{48x^{2}y^{3}}\)
- step1: Write as a product:
\(\sqrt{16\times 3x^{2}y^{3}}\)
- step2: Write in exponential form:
\(\sqrt{4^{2}\times 3x^{2}y^{3}}\)
- step3: Rewrite the exponent:
\(\sqrt{4^{2}\times 3x^{2}y^{2+1}}\)
- step4: Expand the expression:
\(\sqrt{4^{2}\times 3x^{2}y^{2}\times y}\)
- step5: Reorder the terms:
\(\sqrt{4^{2}x^{2}y^{2}\times 3y}\)
- step6: Use the properties of radicals:
\(\sqrt{4^{2}x^{2}y^{2}}\times \sqrt{3y}\)
- step7: Simplify the root:
\(4xy\sqrt{3y}\)
Calculate or simplify the expression \( 4|x y| \sqrt{y} \).
Simplify the expression by following steps:
- step0: Solution:
\(4\left|xy\right|\times \sqrt{y}\)
Calculate or simplify the expression \( 4 x y \sqrt{3} \).
Simplify the expression by following steps:
- step0: Solution:
\(4xy\sqrt{3}\)
- step1: Calculate:
\(4\sqrt{3}\times xy\)
Calculate or simplify the expression \( 4 x y \sqrt{3 y} \).
Simplify the expression by following steps:
- step0: Solution:
\(4xy\sqrt{3y}\)
Calculate or simplify the expression \( 4|x y| \sqrt{3 y} \).
Simplify the expression by following steps:
- step0: Solution:
\(4\left|xy\right|\times \sqrt{3y}\)
The simplified forms of the given expressions are:
1. \( \sqrt{48 x^{2} y^{3}} = 4xy\sqrt{3y} \)
2. \( 4|x y| \sqrt{y} = 4\left|xy\right|\times \sqrt{y} \)
3. \( 4 x y \sqrt{3} = 4\sqrt{3}\times xy \)
4. \( 4 x y \sqrt{3 y} = 4xy\sqrt{3y} \)
5. \( 4|x y| \sqrt{3 y} = 4\left|xy\right|\times \sqrt{3y} \)
Quick Answer
1. \( \sqrt{48 x^{2} y^{3}} = 4xy\sqrt{3y} \)
2. \( 4|x y| \sqrt{y} = 4\left|xy\right|\times \sqrt{y} \)
3. \( 4 x y \sqrt{3} = 4\sqrt{3}\times xy \)
4. \( 4 x y \sqrt{3 y} = 4xy\sqrt{3y} \)
5. \( 4|x y| \sqrt{3 y} = 4\left|xy\right|\times \sqrt{3y} \)
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