What is sqrt(45^2-30^2) ?

The solution to sqrt(45^2-30^2) is 15sqrt(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sqrt(45^2-30^2)

simplify

4 5^{2} - 3 0^{2}

155

Decimal Notation

33.54101 \dots

Solution steps

4 5^{2} - 3 0^{2}

4 5^{2} - 3 0^{2} = 1125

= 1125

Prime factorization of

1125 : 3^{2} \cdot 5^{3}

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

Apply exponent rule:

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

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

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

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

= 3^{2} 5^{2} 5

Apply radical rule:

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

3^{2} = 3

= 3 5^{2} 5

Apply radical rule:

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

5^{2} = 5

= 3 \cdot 55

Multiply the numbers:

3 \cdot 5 = 15

= 155

3^{- 6} \cdot 3^{4}

(2 7^{p - 1} \cdot 9^{3 - p})^{2}

\frac{- x ^{2}}{2}

\frac{2}{5} \div \frac{3}{10}

\frac{86}{4}