What is sqrt(3)(2-sqrt(24)) ?

The solution to sqrt(3)(2-sqrt(24)) is (2-2sqrt(6))sqrt(3)

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simplify sqrt(3)(2-sqrt(24))

simplify

3 (2 - 24)

(2 - 26) 3

Decimal Notation

- 5.02117 \dots

Solution steps

3 (2 - 24)

Prime factorization of

24 : 2^{3} \cdot 3

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

Apply exponent rule:

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

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

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

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

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

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

Apply radical rule:

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

2^{2} = 2

= 3 (2 - 2 2 \cdot 3)

Multiply the numbers:

2 \cdot 3 = 6

= 3 (2 - 26)

= (2 - 26) 3

- 6 m^{2} + 18 m - 36

\frac{1}{2} x - 6 = 5

(- 3 + 2 i) (7 + 3 i)

- \frac{9}{3}

x^{2} + 5 x y - 6 y^{2}

What is sqrt(3)(2-sqrt(24)) ?
The solution to sqrt(3)(2-sqrt(24)) is (2-2sqrt(6))sqrt(3)