What is sqrt(12^2-6^2) ?

The solution to sqrt(12^2-6^2) is 6sqrt(3)

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simplify sqrt(12^2-6^2)

simplify

1 2^{2} - 6^{2}

63

Decimal Notation

10.39230 \dots

Solution steps

1 2^{2} - 6^{2}

1 2^{2} - 6^{2} = 108

= 108

Prime factorization of

108 : 2^{2} \cdot 3^{3}

= 2^{2} \cdot 3^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{2} \cdot 3^{3} = 2^{2} \cdot 3^{2} \cdot 3

= 2^{2} \cdot 3^{2} \cdot 3

2^{2} \cdot 3^{2} \cdot 3 = 2^{2} 3^{2} 3

= 2^{2} 3^{2} 3

Apply radical rule:

a^{2} = a, a \geq 0

2^{2} = 2

= 2 3^{2} 3

Apply radical rule:

a^{2} = a, a \geq 0

3^{2} = 3

= 2 \cdot 33

Multiply the numbers:

2 \cdot 3 = 6

= 63

\frac{1}{x} + 4

\frac{1}{x} - 3

2 \cdot \frac{9}{16}

3 \cdot 81

\frac{0}{100}