Question

Va rog repede! Dau coroana.

Answer 1

$1.a)\sqrt{2^{2}}\cdot3^{4}=2\cdot81=162 \\ \\b) \sqrt{3^{4}\cdot7^{4} }=3^{2}\cdot7^{2}=9\cdot49=441\\ \\c)\sqrt[3]{3^{3}\cdot 5^{6}}=3\sqrt[3]{ 5^{2\cdot3}}=3\cdot5^{2} =3\cdot25=75$

$2.a)\sqrt{250}=\sqrt{5^{2}\cdot2\cdot5} =5\sqrt{10}$

$b)\sqrt[3]{135}=\sqrt[3]{3^{3}\cdot5}=3\cdot\sqrt[3]{5}$

Answer 2

$1) \\ \\ a) { \sqrt{2} }^{2} \times {3}^{4} = 2 \times 81 = 162$

$b) \sqrt{ {3}^{4} \times {7}^{4} } = {3}^{2} \times {7}^{2} = (3 \times 7) ^{2} = {21}^{2}$

$c) \sqrt[3]{ {3}^{3} \times {5}^{6} } = \sqrt[3]{ {3}^{3} } \sqrt[3]{ {5}^{6} } = 3 \times {5}^{2} = 3 \times 25 = 75$

$2) \\ \\ a) \sqrt{250} = \sqrt{2 \times 5 \times 5 \times 5} = \sqrt{(5 \times 5) \times 2 \times 5} = \sqrt{ {5}^{2} \times 2 \times 5 } = 5 \sqrt{2 \times 5} = 5 \sqrt{10}$

$b) \sqrt[3]{135} = \sqrt[3]{3 \times 3 \times 3 \times 5} = \sqrt[3]{(3 \times 3 \times 3) \times 5} = \sqrt[3]{ {3}^{3} \times 5 } = 3 \sqrt[3]{5}$