simplify: 5 / sqrt (7) - sqrt(2)
a) sqrt (7) - sqrt (2)
b) sqrt(7) + sqrt (2)
c) 5 sqrt((7) + sqrt (2))/ 9
d) 1
The way you typed it, none of these answers are correct,
BUT
if you mean
5/(√7 - √2) then
5/(√7 - √2)
=5/(√7 - √2) * (√7+√2)/(√7+√™)
= (5√7 + 5√2)/5
= √7 + √2
To simplify the expression 5 / sqrt(7) - sqrt(2), we need to rationalize the denominator by getting rid of the square root in the denominator.
To do this, we multiply the numerator and denominator by the conjugate of the denominator, which is sqrt(7) + sqrt(2).
So, the expression becomes:
(5 / sqrt(7) - sqrt(2)) * (sqrt(7) + sqrt(2)) / (sqrt(7) + sqrt(2))
Using the distributive property, we can simplify this to:
(5 * sqrt(7) + 5 * sqrt(2) - sqrt(2) * sqrt(7) - sqrt(2) * sqrt(2)) / (sqrt(7) + sqrt(2))
The square root of 7 multiplied by the square root of 2 is the square root of 14. The square root of 2 multiplied by the square root of 2 is 2. So, the expression further simplifies to:
(5 * sqrt(7) + 5 * sqrt(2) - sqrt(14) - 2) / (sqrt(7) + sqrt(2))
Combining the like terms in the numerator, we get:
(5 * sqrt(7) - sqrt(14) + 5 * sqrt(2) - 2) / (sqrt(7) + sqrt(2))
Simplifying the numerator gives:
(5 * sqrt(7) - sqrt(14) + 5 * sqrt(2) - 2)
Therefore, the simplified expression 5 / sqrt(7) - sqrt(2) is:
(5 * sqrt(7) - sqrt(14) + 5 * sqrt(2) - 2) / (sqrt(7) + sqrt(2))
The answer is not one of the provided options.
To simplify the expression 5 / sqrt(7) - sqrt(2), we can follow these steps:
Step 1: Rationalize the denominator of the fraction sqrt(7).
The denominator of the fraction is sqrt(7). To rationalize it, we multiply both the numerator and denominator by sqrt(7).
5 / sqrt(7) - sqrt(2) can be written as (5 * sqrt(7)) / (sqrt(7) * sqrt(7)) - sqrt(2).
Simplifying further, we get (5 * sqrt(7)) / 7 - sqrt(2).
Step 2: Combine like terms.
The expression becomes (5 * sqrt(7) - sqrt(2)) / 7.
So, the simplified expression for 5 / sqrt(7) - sqrt(2) is (5 * sqrt(7) - sqrt(2)) / 7.
Therefore, the correct answer is d) 1.