If y -7-7-8-2 -7-7- then the value of y will be-A- 1 - -7- 8-2 -7D- -7-1

The correct option is A 1 y=√(√(7)+7+√(8+2√(7))) √(7) Here, 8+2√(7)=7+1+2√(7)=(√(7)+1)^2 y=√(√(7)+7+√((√(7)+1)^2)) √(7) y=√(√(7)+7+(√(7)+1)) √(7) y=√(2√(7)+7+1 ...

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Byju's Answer

Standard X

Mathematics

Solving a Quadratic Equation by Completion of Squares Method

If y =√√7+7+√...

Question

If $y = \sqrt{\sqrt{7} + 7 + \sqrt{8 + 2 \sqrt{7}}} - \sqrt{7}$ , then the value of y will be:

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$\sqrt{7}$

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$8 - 2 \sqrt{7}$

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$\sqrt{7} - 1$

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Solution

The correct option is A
1

$y = \sqrt{\sqrt{7} + 7 + \sqrt{8 + 2 \sqrt{7}}} - \sqrt{7}$
Here, $8 + 2 \sqrt{7} = 7 + 1 + 2 \sqrt{7} = (\sqrt{7} + 1)^{2}$
$y = \sqrt{\sqrt{7} + 7 + \sqrt{(\sqrt{7} + 1)^{2}}} - \sqrt{7}$
$y = \sqrt{\sqrt{7} + 7 + (\sqrt{7} + 1)} - \sqrt{7}$
$y = \sqrt{2 \sqrt{7} + 7 + 1} - \sqrt{7}$
$y = \sqrt{(\sqrt{7} + 1)^{2}} - \sqrt{7}$
$y = (\sqrt{7} + 1) - \sqrt{7}$
$y = 1$

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If y=√√7+7+√8+2√7−√7, then the value of y will be:

The correct option is A 1 y=√√7+7+√8+2√7−√7 Here, 8+2√7=7+1+2√7=(√7+1)2 y=√√7+7+√(√7+1)2−√7 y=√√7+7+(√7+1)−√7 y=√2√7+7+1−√7 y=√(√7+1)2−√7 y=(√7+1)−√7 y=1

If $y = \sqrt{\sqrt{7} + 7 + \sqrt{8 + 2 \sqrt{7}}} - \sqrt{7}$ , then the value of y will be: