Question

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Answer 1

Answer:

Part 1) $2\sqrt{6}$

Part 2) $4\sqrt{5}$

Part 3) $36\sqrt{10}$

Part 4) $15\sqrt{5}$

Part 5) $20\sqrt{5}$

Part 6) $9\sqrt{2}$

Step-by-step explanation:

Part 1) we have

$\sqrt{24}$

we know that

$24=(2^{3})(3)$

Remember that

$\sqrt{a^{2}}=a$

substitute

$\sqrt{(2^{3})(3)}=\sqrt{(2^{2})(2)(3)}=2\sqrt{6}$

Part 2) we have

$\sqrt{80}$

we know that

$80=(2^{4})(5)$

Remember that

$\sqrt{a^{2}}=a$

substitute

$\sqrt{(2^{4})(5)}$

we have that

$(2^{4})=(2^{2})^{2}=4^{2}$

substitute

$\sqrt{(4^{2}(5)}=4\sqrt{5}$

Part 3) we have

$12\sqrt{90}$

we know that

$90=(2)(3^{2})(5)$

Remember that

$\sqrt{a^{2}}=a$

substitute

$12\sqrt{(2)(3^{2})(5)}=12\sqrt{(3^{2})(5)(2)}=(12)(3)\sqrt{(5)(2)}=36\sqrt{10}$

Part 4) we have

$3\sqrt{125}$

we know that

$125=(5^{3})$

Remember that

$\sqrt{a^{2}}=a$

substitute

$3\sqrt{(5^{3})}=3\sqrt{(5^{2})(5)}=(3)(5)\sqrt{5}=15\sqrt{5}$

Part 5)  we have

$2\sqrt{500}$

we know that

$500=(2^{2})(5^{3})$

Remember that

$\sqrt{a^{2}}=a$

substitute

$2\sqrt{(2^{2})(5^{3})}=2\sqrt{(2^{2})(5^{2})(5)}=(2)(2)(5)\sqrt{5}=20\sqrt{5}$

Part 6) we have

$\sqrt{162}$

we know that

$162=(2)(3^{4})$

Remember that

$\sqrt{a^{2}}=a$

substitute

$\sqrt{(2)(3^{4})}=\sqrt{(2)(3^{2})^{2}}=(3^{2})\sqrt{(2)}=9\sqrt{2}$