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

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

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Popular >

simplify sqrt(7-\sqrt{48)}

simplify

7 - 48

2 - 3

Decimal Notation

0.26794 \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 exponent rule:

(- a)^{n} = a^{n},

n

is even

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

= (2 - 3)^{2}

Apply radical rule:

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

= 2 - 3

sin^{2} (θ)

\frac{2 x}{2}

(2 x + 9) + (4 x - 3)

5 (5 u - 2 v) + 0.4 v - 10 (- 9 v - 10 u)

(27 a^{6})^{\frac{2}{3}}