you could use a calculator or the best way to know is find a perfect square that multiplies another number to make that number. for example, square root of 175 (√175) = √25 times √7. then take the square root of the perfect square and multiply it by the square root. (√25 = 5) so the answer is 5 times √7. or 5√7
To simplify the square root of 175, we look for the largest perfect square factor of 175. We find that 25 is a perfect square that divides 175. We can express 175 as 25*7. Taking the square root of both terms, we get √25 * √7, and since the square root of 25 is 5, we simplify this to 5√7. So, the simplified form of √175 is 5√7.
Step-by-Step Simplification
Factor 175 into 25*7, where 25 is a perfect square.
Write √175 as √(25*7).
Simplify √25 to 5 because 5*5 = 25.
The final simplified result is 5√7.
Remember that simplifying the square root involves finding the largest perfect square factor, taking its square root, and then multiplying it by the square root of the remaining factor.
To simplify the square root of 175, first find its prime factors, which gives you 175 = 5 2 × 7 . Then, take the square root of the perfect square to obtain 175 = 5 7 . Hence, the simplified form is 5 7 .
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