What is sqrt(a^2b^2+b^2c^2) ?

The solution to sqrt(a^2b^2+b^2c^2) is bsqrt(a^2+c^2)

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simplify sqrt(a^2b^2+b^2c^2)

simplify

a^{2} b^{2} + b^{2} c^{2}

b a^{2} + c^{2}

Solution steps

a^{2} b^{2} + b^{2} c^{2}

Factor out common term

b^{2}

= b^{2} (a^{2} + c^{2})

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

b^{2} (a^{2} + c^{2}) = b^{2} a^{2} + c^{2}

= b^{2} a^{2} + c^{2}

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

b^{2} = b

= b a^{2} + c^{2}

(\frac{11}{8}) (- \frac{3}{10})

\frac{5}{4} \div 10

- 0.08 \cdot 20 + 800

3 i (2 + 3 i)

(0.11)^{2}

What is sqrt(a^2b^2+b^2c^2) ?
The solution to sqrt(a^2b^2+b^2c^2) is bsqrt(a^2+c^2)