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aliya0001 [1]
4 years ago
9

Need help with these question give me tha answer

Mathematics
1 answer:
lidiya [134]4 years ago
6 0

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}

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