Question

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Answer 1

$1) sqrt{5} times sqrt{20} = sqrt{5 times 20} = sqrt{100} = 10$
$2) sqrt{125} div sqrt{5} = sqrt{125 div 5} = sqrt{25} = 5$
$3) {( sqrt{7} )}^{2} = sqrt{7} times sqrt{7} = sqrt{7 times 7} = sqrt{49} = 7$
$4) frac{ {10}^{3} }{ sqrt{10000} } = frac{1000}{100} = 10$
$5){(5 sqrt{2})}^{2} = {5}^{2} times { (sqrt{2}) }^{2} = 25 times 2 = 100$
$sqrt{50} - 2 sqrt{2} = sqrt{2 times 25} - 2 sqrt{2} = 5 sqrt{2} - 2 sqrt{2} = 3 sqrt{2}$
7)
$sqrt{3} + sqrt{3} + sqrt{3} = 3 sqrt{3}$
8)
$18 sqrt{5} times 2 sqrt{5} = 18 times 2 times 5 = 180$
9)
$sqrt{ {15}^{2} } = 15$
10)
$sqrt{72} = sqrt{8 times 9} = sqrt{2 times 4} times sqrt{9} = 2 times 3 sqrt{2} = 6 sqrt{2}$
11)
$sqrt{ {8}^{4} } div 16 = {8}^{2} div 16 = 64 div 16 = 4$
12)
$sqrt{ {(5 - sqrt{50}) }^{2} } = 5 - sqrt{50}$
13)
$sqrt{ {16}^{2} - {9}^{2} } = sqrt{(16 - 9)(16 + 9)} = \ sqrt{7 times 25} = 5 sqrt{7}$
14)
$sqrt{ {3}^{2} times {2}^{4} times 9 } = 3 times 4 times 3 = 36$
15)
$3 sqrt{2} = sqrt{2 times {3}^{2} } = sqrt{18}$
16)
$frac{ sqrt{24} }{ sqrt{6} } = sqrt{ frac{24}{6} } = sqrt{4} = 2$
17)
$sqrt{125} times sqrt{8} = sqrt{5 times 25 times 4 times 2} = 10 sqrt{10}$