Simplify 2 over the square root of 5.
To simplify 2 over the square root of 5, we need to rationalize the denominator. We can do this by multiplying both the numerator and denominator by the square root of 5:
2/sqrt(5) x sqrt(5)/sqrt(5) = 2 sqrt(5)/5
Therefore, 2 over the square root of 5 simplifies to 2 sqrt(5)/5.
simplify -11 multiplied by the square root of 112
To simplify -11 multiplied by the square root of 112, we can first simplify the square root of 112. We can do this by factoring out the perfect square 16 from 112:
√112 = √(16 x 7) = √16 x √7 = 4√7
Now we can substitute 4√7 into the expression:
-11 x 4√7 = -44√7
Therefore, -11 multiplied by the square root of 112 simplifies to -44√7.
simplify (17 multiplied by the square root of 17) (-9 multiplied by the square root of 17)
simplify 6 divided by the square root of 3 plus 2
To simplify 6 divided by the square root of 3 plus 2, we need to rationalize the denominator. We can do this by multiplying both the numerator and denominator by the conjugate of the denominator, which is the square root of 3 minus 2:
6/(sqrt(3) + 2) x (sqrt(3) - 2)/(sqrt(3) - 2) = 6(sqrt(3) - 2)/(3 - 4)
Note that we used the difference of squares identity, (a + b)(a - b) = a^2 - b^2, to simplify the denominator.
Simplifying the denominator further, we have:
6(sqrt(3) - 2)/(-1) = -6(sqrt(3) - 2)
Therefore, 6 divided by the square root of 3 plus 2 simplifies to -6(sqrt(3) - 2).
To simplify (17 multiplied by the square root of 17) (-9 multiplied by the square root of 17), we can use the distributive property of multiplication:
(17 √17) (-9 √17) = -153 √(17 x 17) = -153 x 17 = -2601
Therefore, (17 multiplied by the square root of 17) (-9 multiplied by the square root of 17) simplifies to -2601.