Question - Solving an Expression with Square Roots
Solution:
The expression given in the image is:√28 - √7 / √3 × √5 / 4To solve it, we first simplify the square roots and then follow the order of operations.√28 can be simplified by recognizing that 28 is 4 times 7, and 4 is a perfect square:√28 = √(4×7) = √4 × √7 = 2√7Now we can rewrite the expression:2√7 - √7 / √3 × √5 / 4Before going further, we should clarify the order of operations. If the expression is meant to be read as:(2√7 - √7) / (√3 × √5 / 4)we should perform the subtraction first, then the multiplication, and finally the division. However, if each square root is to be divided or multiplied individually before subtracting, we need parentheses to indicate which operations to perform first.Assuming it is the former, and the subtraction is to be done first, followed by the division and multiplication:First, subtract √7 from 2√7:2√7 - √7 = √7Next, multiply √3 and √5:√3 × √5 = √(3×5) = √15Now we have:√7 / √15 × 1 / 4To simplify this we will write √7 as √7/1 and do the division by multiplying by the reciprocal:√7/1 × 1/√15 × 1/4Now, to simplify √7/√15, we get:√7 / √15 = √(7/15) = √(0.4667)And when we multiply by 1/4:√(7/15) × 1/4 = √(7/60)The last step cannot be nicely simplified without a calculator as 7/60 is not a perfect square, but you can leave your answer as √(7/60) or approximate it with a calculator if necessary.
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