What is sqrt(97-56\sqrt{3)} ?

The solution to sqrt(97-56\sqrt{3)} is 7-4sqrt(3)

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simplify sqrt(97-56\sqrt{3)}

simplify

97 - 563

7 - 43

Decimal Notation

0.07179 \dots

Solution steps

97 - 563

= 48 - 563 + 49

= 16 \cdot 3 - 563 + 49

= (16)^{2} (3)^{2} - 563 + (49)^{2}

16 = 4

49 = 7

= 4^{2} (3)^{2} - 563 + 7^{2}

2 \cdot 43 \cdot 7 = 563

= (43)^{2} - 2 \cdot 43 \cdot 7 + 7^{2}

Apply Perfect Square Formula:

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

(43)^{2} - 2 \cdot 43 \cdot 7 + 7^{2} = (43 - 7)^{2}

= (43 - 7)^{2}

Apply exponent rule:

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

n

is even

(43 - 7)^{2} = (7 - 43)^{2}

= (7 - 43)^{2}

Apply radical rule:

(7 - 43)^{2} = 7 - 43

= 7 - 43

x \frac{1}{4}

5 x^{2} + 36 x + 7

- (- 9 c - 0.8 d - 1)

lo g_{243} (3)

4 r + 5 p - 6 r + 7