Question

if root 2 =1.414,then find the value of 3root 32-2root 50+4 root 128-20 root 18

Answer 1

I hope it helps to u

Answer 2

$Given \: \sqrt{2} = 1.414 \: ---(1)$

$i ) \sqrt{32}\\ = \sqrt{ 2\times 2 \times 2\times 2\times 2 } \\= 4 \sqrt{2}$

$ii ) \sqrt{50}\\ = \sqrt{ 2\times 5 \times 5} \\= 5 \sqrt{2}$

$iii ) \sqrt{128}\\ = \sqrt{ 2\times 2 \times 2\times 2\times 2 \times 2 \times 2} \\= 8 \sqrt{2}$

$iv) \sqrt{18}\\ = \sqrt{ 2\times 3 \times 3}\\= 3\sqrt{2}$

$Now, \red {Value \: of \: 3\sqrt{32} - 2\sqrt{50} + 4\sqrt{128}-20\sqrt{18}} \\= 3\times 4\sqrt{2} - 2\times 5\sqrt{2} + 4 \times 8\sqrt{2} -20\times 3\sqrt{2} \\= 12\sqrt{2} - 10\sqrt{2} + 32\sqrt{2} -60 \sqrt{2} \\= ( 12-10+32-60)\sqrt{2} \\= -26\sqrt{2} \\= -26 \times 1.414\: [ From \: (1) ] \\= - 36.764$

Therefore.,

$\red {Value \: of \: 3\sqrt{32} - 2\sqrt{50} + 4\sqrt{128}-20\sqrt{18}}\green {= - 36.764}$

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