Question #91306

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Question #91306

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Answer 1 · 2017-02-06T13:32:31

$= 12 \sqrt{2} \times m^{3} k^{3}$ $=12sqrt2xxm^3k^3$

Explanation:

Note one of the laws of indices:

$\sqrt[q]{x^{p}} = x^{\frac{p}{q}}$ $root(q)(x^p) = x ^(p/q)$

In words this will say " to find a root, divide the index by the root "

So $\sqrt{x^{10}} = x^{5} \sqrt[3]{x^{9}} = x^{3}$ $sqrt (x^10) = x^5" "root3(x^9) = x^3$

It is useful to write the numbers as the product of the prime factors.

$324 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 = 2^{2} \times 3^{4}$ $324 = 2xx2xx3xx3xx3xx3 = 2^2 xx 3^4$

$64 = 2^{6}$ $64 = 2^6$

Use these factors instead of $324 and 64$ $324 and 64$

$\sqrt[4]{324 m^{12}} \times \sqrt[3]{64 k^{9}}$ $root(4)(324m^12) xx root3(64k^9)$

$= \sqrt[4]{2^{2} \times 3^{4} \times m^{12}} \times \sqrt[3]{2^{6} \times k^{9}}$ $=root(4)(2^2xx3^4xxm^12) xx root3(2^6xxk^9)$

Now divide each index by the root you want to find.

$= 2^{\frac{1}{2}} \times 3 \times m^{3} \times 2^{2} \times k^{3} \leftarrow$ $=2^(1/2) xxcolor(blue)(3) xxm^3 xxcolor(blue)(2^2) xx k^3" "larr$ multiply the numbers

$= 12 \sqrt{2} \times m^{3} k^{3} (2^{\frac{1}{2}} = \sqrt{2})$ $=color(blue)(12) sqrt2xx m^3k^3" "(2^(1/2) = sqrt2)$

Hope this helps?

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Question #91306

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