Question

xD*





The value of
$\sqrt{7 + 2 \sqrt{10} }$
equal to:​

Answer 1

To Find:

The value of the expression given as:

$\sqrt{7 + 2 \sqrt{5} }$

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♦Solution♦

The given expression must be simplified to find the value easily without any error during calculation, For doing so:

$\sqrt{7 + 2 \sqrt{10} } = \sqrt{2 + 5 + 2 \sqrt{5 \times 2} }$

$\sqrt{2 + 5 + 2 \sqrt{5}. \sqrt{2} }$

$or \: \sqrt{2 + 2 \sqrt{2} . \sqrt{5} + 5}$

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Now, We can see that, in the above calculated expression,

a=√2, b=√5, 2ab= 2√2.√5

So, on applying the rule of

(a+b)²=a²+2ab+b²

We get:

$\sqrt{7 + 2 \sqrt{10} } = \sqrt{( \sqrt{2} + \sqrt{5}) {}^{2} }$

Answer:

» $\sqrt{7 + 2 \sqrt{10} } = ( \sqrt{2} + \sqrt{5} )$

Now, As, √2=1.414 and, √2=2.236

Thus,

$\sqrt{7 + 2 \sqrt{10} } = (1.414) + (2.236)$

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★Answer★

$\sqrt{7 + 2 \sqrt{10} } = 3.65 \: (approx)$

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Verification:

The value of √10=3.162

$∴ \: \sqrt{7 + 2 \sqrt{10} } = \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{ 7 + 2(3.162)} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{7 + 6.324} \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{13.324} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.650 \: (approx)$