simplify 40^{1/2}

Solution

simplify

4 0^{\frac{1}{2}}

2 \cdot 1 0^{\frac{1}{2}}

Decimal Notation

6.32455 \dots

Solution steps

4 0^{\frac{1}{2}}

Prime factorization of

40 : 2^{3} \cdot 5

= (2^{3} \cdot 5)^{\frac{1}{2}}

Apply exponent rule:

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

2^{3} \cdot 5 = 2^{2} \cdot 2 \cdot 5

= (2^{2} \cdot 2 \cdot 5)^{\frac{1}{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2^{2} \cdot 2 \cdot 5)^{\frac{1}{2}} = (2^{2})^{\frac{1}{2}} (2 \cdot 5)^{\frac{1}{2}}

= (2^{2})^{\frac{1}{2}} (2 \cdot 5)^{\frac{1}{2}}

(2^{2})^{\frac{1}{2}} = 2

= 2 (2 \cdot 5)^{\frac{1}{2}}

Multiply the numbers:

2 \cdot 5 = 10

= 2 \cdot 1 0^{\frac{1}{2}}

2 \cdot π \cdot 60

\frac{\frac{3 n ^{2} + 9 n}{2 n}}{\frac{n + 3}{4}}

2 lo g_{10} (100) + 3 lo g_{3} (9) - 4 lo g_{10} (10)

9 (- 4 x^{5})^{2}

- 8 \cdot (- 3)