If y - -7- 7 -8-2-7-7 then find the value of y-

√((√(7))+ 7 +√((8+2√(7))))) 8+2√(7)= 1+7+2 √(7)=(√(7)+1)^2 On solving for, we get √((√(7))+7+√(((√(7)+1)^2)) √(7)) √((√(7))+7+√(7)+1) √(7) √(7+2√(7)+1) √(7) √( ...

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Byju's Answer

Standard IX

Mathematics

Multiplication of Numbers with Square Roots

If y = √√7+ 7...

Question

If y = $\sqrt{(\sqrt{7}) + 7 + \sqrt{(8 + 2 \sqrt{7}}))} - \sqrt{7}$ then find the value of y.

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Solution

$\sqrt{(\sqrt{7}) + 7 + \sqrt{(8 + 2 \sqrt{7}}))} 8 + 2 \sqrt{7} = 1 + 7 + 2 \sqrt{7} = (\sqrt{7} + 1)^{2}$
On solving for, we get
$\sqrt{(\sqrt{7}) + 7 + \sqrt{((\sqrt{7} + 1)^{2})} - \sqrt{7}} \sqrt{(\sqrt{7}) + 7 + \sqrt{7} + 1} - \sqrt{7} \sqrt{7 + 2 \sqrt{7} + 1} - \sqrt{7} \sqrt{(\sqrt{7} + 1)^{2}} - \sqrt{7} \sqrt{7} + 1 - \sqrt{7} = 1$

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If y = √(√7)+7+√(8+2√7))−√7 then find the value of y.

√(√7)+7+√(8+2√7))8+2√7=1+7+2√7=(√7+1)2 On solving for, we get √(√7)+7+√((√7+1)2)−√7√(√7)+7+√7+1−√7√7+2√7+1−√7√(√7+1)2−√7√7+1−√7=1

If y = $\sqrt{(\sqrt{7}) + 7 + \sqrt{(8 + 2 \sqrt{7}}))} - \sqrt{7}$ then find the value of y.