How do you simplify this?
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/ 1 /
5/ - * /18
/ 3 /
The hyphens and slashes are meant to be radical signs.
Thank you!
To simplify the expression, you need to evaluate the square root of the fraction (1/5) and then multiply it by the reciprocal of the square root of the fraction (3/18). Here are the steps to simplify it:
Step 1: Evaluate the square root of the fraction (1/5).
- The square root of 1/5 can be written as √(1/5).
Step 2: Simplify the square root expression.
- To simplify, we can multiply the numerator and denominator by the same number to get rid of the fraction. In this case, we can multiply both the numerator and denominator by √5 to rationalize the denominator.
- √(1/5) = (√(1) * √(5)) / (√(5) * √(5)) = (√5) / 5.
Step 3: Evaluate the reciprocal of the square root of the fraction (3/18).
- The reciprocal of √(3/18) is 1 / (√(3/18)).
- Similarly, we can rationalize the denominator by multiplying both the numerator and denominator by √18.
- 1 / (√(3/18)) = (1 * √18) / (√(18) * √(18)) = √18 / 18.
Step 4: Multiply the two simplified expressions from Step 2 and Step 3.
- (√5) / 5 * (√18) / 18
- To multiply these two fractions, multiply the numerators and multiply the denominators separately.
- (√5 * √18) / (5 * 18)
- Simplify the numerator and denominator separately by multiplying the square roots and simplifying the multiplication.
- (√(5 * 18)) / 90
- (√90) / 90
So, the simplified expression is (√90) / 90.