What is 3/(sqrt(40)) ?

The solution to 3/(sqrt(40)) is 3/(2sqrt(10))

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simplify 3/(sqrt(40))

simplify

\frac{3}{40}

\frac{3}{2 10}

Decimal Notation

0.47434 \dots

Solution steps

\frac{3}{40}

Prime factorization of

40 : 2^{3} \cdot 5

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

Apply exponent rule:

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

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

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

Apply radical rule:

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

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

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

Apply radical rule:

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

2^{2} = 2

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

Multiply the numbers:

2 \cdot 5 = 10

= \frac{3}{2 10}

(3^{3})^{4}

\frac{x}{2} - x

\frac{( 2 d ) ^{3}}{2 d ^{5}}

- \frac{7}{- 1}

(3 + 2 i) (1 - 4 i)