Evaluate 34 square root of 975

Problem

34√(,975)

Solution

1. Identify the radicand and look for perfect square factors. The number 975 ends in 75 so it is divisible by 25

2. Factor the radicand into a product of a perfect square and another integer.

975=25⋅39

3. Apply the product property of square roots to separate the factors.

√(,975)=√(,25⋅39)

√(,975)=√(,25)⋅√(,39)

4. Simplify the square root of the perfect square.

√(,25)=5

√(,975)=5√(,39)

5. Substitute this simplified form back into the original expression.

34√(,975)=34⋅5√(,39)

6. Multiply the coefficients outside the radical.

34⋅5=170

Final Answer

34√(,975)=170√(,39)

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