What is sqrt(((5-120x)^2+(150x)^2)) ?

The solution to sqrt(((5-120x)^2+(150x)^2)) is 5sqrt(1-48x+1476x^2)

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simplify sqrt(((5-120x)^2+(150x)^2))

simplify

((5 - 120 x)^{2} + (150 x)^{2})

5 1 - 48 x + 1476 x^{2}

Solution steps

(5 - 120 x)^{2} + (150 x)^{2}

Apply rule:

(a) = a

((5 - 120 x)^{2} + (150 x)^{2}) = (5 - 120 x)^{2} + (150 x)^{2}

= (5 - 120 x)^{2} + (150 x)^{2}

Simplify

(5 - 120 x)^{2} + (150 x)^{2} : 25 - 1200 x + 36900 x^{2}

= 25 - 1200 x + 36900 x^{2}

Factor out common term

25 : 25 (1 - 48 x + 1476 x^{2})

= 25 (1 - 48 x + 1476 x^{2})

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

25 (1 - 48 x + 1476 x^{2}) = 25 1 - 48 x + 1476 x^{2}

= 25 1 - 48 x + 1476 x^{2}

25 = 5

= 5 1 - 48 x + 1476 x^{2}

What is sqrt(((5-120x)^2+(150x)^2)) ?
The solution to sqrt(((5-120x)^2+(150x)^2)) is 5sqrt(1-48x+1476x^2)