how do you simplify the square root of 50xsquared?

Answer 1

Nikki:

sqrt(50x^2) = sqrt(50)*sqrt(x^2)
= sqrt(25)*sqrt(2)*x
= 5x*sqrt(2)

Good luck!

Answer 2

Easy. Stop using the √ symbol and start thinking about the square root as what it is, an exponent of 1/2.

√(50x^2) is really (50x^2)^(1/2)

There as a rule about exponents
(ab)^p = (a^p)(b^p)

So
(50x^2)^(1/2) = [50^(1/2)][(x^2)^(1/2)]
={[25^(1/2)] [2^(1/2)]} {x^[(2)(1/2)]}
because of the rule already mentioned, and also because of a rule that says (n^p)^q = n^(pq)

We know that 25^(1/2) = 5 (or -5). We also know that x^[(2)(1/2)]=x^1 and x^1 = x (or -x)

So we have
(50x^2)^(1/2) = [50^(1/2)][(x^2)^(1/2)]
={[25^(1/2)] [2^(1/2)]} {x^[(2)(1/2)]} =
(5)(x)[2^(1/2)] but we don't know if it's positive or negative.

Answer 3

√(50x^2)
= √(2*5^2*x^2)
= 5|x|√2
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You have to use the absolute sign for x. Otherwise, it is not right. For example, if x = -1, √(50x^2) = 5√2. But 5x√2 = -5√2.

Answer 4

since this is the same as asking for the square root of
5^2 x^2
the answer would be 5|x|
the absolute value sign is necessary in case x is negative

Answer 5

50 x^2= 25 x^2 * 2
sqrt of 25 x^2 *2
5x sqrt 2

Answer 6

use a calculater
sq.rt of 50x^2 = 7.0710678118654752440084436210485x