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Answer :
Let's simplify the expression [tex]\(\sqrt{49 y^8} \times \sqrt{9 x^{18}}\)[/tex].
1. Simplify each square root separately:
- For [tex]\(\sqrt{49 y^8}\)[/tex]:
- [tex]\(\sqrt{49} = 7\)[/tex], since [tex]\(49\)[/tex] is a perfect square.
- [tex]\(\sqrt{y^8} = y^{8/2} = y^4\)[/tex], because [tex]\(\sqrt{y^8}\)[/tex] is the same as having [tex]\(y^4 \cdot y^4\)[/tex], and you take one [tex]\(y^4\)[/tex] outside the square root.
Therefore, [tex]\(\sqrt{49 y^8} = 7y^4\)[/tex].
- For [tex]\(\sqrt{9 x^{18}}\)[/tex]:
- [tex]\(\sqrt{9} = 3\)[/tex], since [tex]\(9\)[/tex] is a perfect square.
- [tex]\(\sqrt{x^{18}} = x^{18/2} = x^9\)[/tex], because [tex]\(\sqrt{x^{18}}\)[/tex] is like having nine pairs of [tex]\(x\)[/tex], and you take one [tex]\(x\)[/tex] from each pair outside the square root.
Therefore, [tex]\(\sqrt{9 x^{18}} = 3x^9\)[/tex].
2. Multiply the simplified parts:
- Multiply the results from the two square roots:
[tex]\[
(7y^4) \times (3x^9) = 21x^9y^4
\][/tex]
Therefore, the simplified expression is [tex]\(21x^9y^4\)[/tex], which corresponds to option B.
1. Simplify each square root separately:
- For [tex]\(\sqrt{49 y^8}\)[/tex]:
- [tex]\(\sqrt{49} = 7\)[/tex], since [tex]\(49\)[/tex] is a perfect square.
- [tex]\(\sqrt{y^8} = y^{8/2} = y^4\)[/tex], because [tex]\(\sqrt{y^8}\)[/tex] is the same as having [tex]\(y^4 \cdot y^4\)[/tex], and you take one [tex]\(y^4\)[/tex] outside the square root.
Therefore, [tex]\(\sqrt{49 y^8} = 7y^4\)[/tex].
- For [tex]\(\sqrt{9 x^{18}}\)[/tex]:
- [tex]\(\sqrt{9} = 3\)[/tex], since [tex]\(9\)[/tex] is a perfect square.
- [tex]\(\sqrt{x^{18}} = x^{18/2} = x^9\)[/tex], because [tex]\(\sqrt{x^{18}}\)[/tex] is like having nine pairs of [tex]\(x\)[/tex], and you take one [tex]\(x\)[/tex] from each pair outside the square root.
Therefore, [tex]\(\sqrt{9 x^{18}} = 3x^9\)[/tex].
2. Multiply the simplified parts:
- Multiply the results from the two square roots:
[tex]\[
(7y^4) \times (3x^9) = 21x^9y^4
\][/tex]
Therefore, the simplified expression is [tex]\(21x^9y^4\)[/tex], which corresponds to option B.
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