Example Question - solving square roots
Here are examples of questions we've helped users solve.
Simplifying Square Roots with Negative Sign
The expression shown in the image is "-√12". To solve this, we will simplify the square root of 12 first and then apply the negative sign. √12 can be broken down into √(4 * 3) = √4 * √3. Since we know that √4 is 2, we have √12 = 2√3. Applying the negative sign to this result, we get: -√12 = -2√3 So, the simplified form of "-√12" is "-2√3".
Solving an Expression with Square Roots
The expression given in the image is: √28 - √7 / √3 × √5 / 4 To 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√7 Now we can rewrite the expression: 2√7 - √7 / √3 × √5 / 4 Before 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 = √7 Next, multiply √3 and √5: √3 × √5 = √(3×5) = √15 Now we have: √7 / √15 × 1 / 4 To simplify this we will write √7 as √7/1 and do the division by multiplying by the reciprocal: √7/1 × 1/√15 × 1/4 Now, 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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