What is sqrt(61-28\sqrt{3)} ?

The solution to sqrt(61-28\sqrt{3)} is 7-2sqrt(3)

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Popular >

simplify sqrt(61-28\sqrt{3)}

simplify

61 - 283

7 - 23

Decimal Notation

3.53589 \dots

Solution steps

61 - 283

= 12 - 283 + 49

= 4 \cdot 3 - 283 + 49

= (4)^{2} (3)^{2} - 283 + (49)^{2}

4 = 2

49 = 7

= 2^{2} (3)^{2} - 283 + 7^{2}

2 \cdot 23 \cdot 7 = 283

= (23)^{2} - 2 \cdot 23 \cdot 7 + 7^{2}

Apply Perfect Square Formula:

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

(23)^{2} - 2 \cdot 23 \cdot 7 + 7^{2} = (23 - 7)^{2}

= (23 - 7)^{2}

Apply exponent rule:

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

n

is even

(23 - 7)^{2} = (7 - 23)^{2}

= (7 - 23)^{2}

Apply radical rule:

(7 - 23)^{2} = 7 - 23

= 7 - 23

\frac{7}{15} + \frac{5}{12}

i^{1999}

2 x^{4} - 3 x^{3} - 15 x^{2} + 32 x - 12

y 54 x^{3} y^{3}

0. 2^{8}