What is sqrt(7+\sqrt{48)} ?

The solution to sqrt(7+\sqrt{48)} is sqrt(3)+2

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simplify sqrt(7+\sqrt{48)}

simplify

7 + 48

3 + 2

Decimal Notation

3.73205 \dots

Solution steps

7 + 48

48 = 43

= 7 + 43

= 3 + 43 + 4

= (3)^{2} + 43 + (4)^{2}

4 = 2

= (3)^{2} + 43 + 2^{2}

23 \cdot 2 = 43

= (3)^{2} + 23 \cdot 2 + 2^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(3)^{2} + 23 \cdot 2 + 2^{2} = (3 + 2)^{2}

= (3 + 2)^{2}

Apply radical rule:

(3 + 2)^{2} = 3 + 2

= 3 + 2

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