How do you simplify #sqrt(32/5)#?

Question

Isaiah Anthony · Accepted Answer

4#sqrt(2/5# 32 is equal to 16 times 2, so 16 can be removed from the radical sign as indicated below: #sqrt(32/5# = 4#sqrt(2/5#. If denominator is required to be simplified, this can be done by multiplying the numerator and the denominator by #sqrt5#.  The result would be 4#sqrt10/5#

Hazel Anglin · Answer

undefined To simplify sqrt(32/5), we can simplify the expression under the square root sign first.

First, we can simplify the fraction 32/5 by dividing the numerator and denominator by their greatest common divisor, which is 1. This gives us 32/5.

Next, we can simplify the square root of 32. We can break down 32 into its prime factors: 32 = 2 * 2 * 2 * 2 * 2.

Since there are two pairs of 2's, we can take one 2 out of the square root sign, which leaves us with 2 * sqrt(2).

Finally, we can rewrite sqrt(2) as a decimal approximation, which is approximately 1.414.

Therefore, the simplified form of sqrt(32/5) is 2 * 1.414, which equals approximately 2.828.