How do you simplify $\sqrt{7 + \sqrt{4}}$ $sqrt(7+sqrt4)$ ?

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Answer 1 · 2015-07-23T22:13:08

You take the square root of $4$ $4$ first, then take the square root of the resulting expression.

Notice that your expression contains the square root of $4$ $4$ , which a perfect square. More specifically,

$4 = 2 \cdot 2 = 2^{2}$ $4 = 2 * 2 = 2""^2$

This means that you can write

$\sqrt{7 + \sqrt{4}} = \sqrt{7 + \sqrt{2^{2}}} = \sqrt{7 + 2} = \sqrt{9}$ $sqrt(7 + sqrt(4)) = sqrt(7 + sqrt(2""^2)) = sqrt(7 + 2) = sqrt(9)$

This time you come across the square root of $9$ $9$ , which is another perfect square.

$9 = 3 \cdot 3 = 3^{2}$ $9 = 3 * 3 = 3""^2$

Therefore, your expression becomes

$\sqrt{9} = \sqrt{3^{2}} = 3$ $sqrt(9) = sqrt(3""^2) = 3$

Put all this together to get

$\sqrt{7 + \sqrt{4}} = \sqrt{7 + 2} = 3$ $sqrt(7 + sqrt(4)) = sqrt(7 + 2) = color(green)(3)$

How do you simplify √7+√4sqrt(7+sqrt4)?