How do you simplify 4 times square root of 3 divided by square root of 2?

Question

Genesis Allen · Accepted Answer

#2sqrt(6)# 4 times square root of 3 divided by square root of 2: #color(white)("XXX")=(4sqrt(3))/sqrt(2)# #color(white)("XXX")=(2*cancel(sqrt(2))*sqrt(2)*sqrt(3))/cancel(sqrt(2))# #color(white)("XXX")=2sqrt(6)#

Eva Abramson · Answer

undefined To simplify 4 times the square root of 3 divided by the square root of 2, you can multiply the numerator and denominator by the conjugate of the denominator, which is the square root of 2. This will eliminate the square root in the denominator. Simplifying further, the expression becomes 4 times the square root of 6 divided by 2, which simplifies to 2 times the square root of 6.

Ethan Adkins · Answer

undefined To simplify $4 \times \sqrt{3} \div \sqrt{2}$, we can rationalize the denominator by multiplying both the numerator and denominator by $\sqrt{2}$:

$$ 4 \times \sqrt{3} \div \sqrt{2} = \frac{4 \times \sqrt{3} \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} $$

This simplifies to:

$$ \frac{4 \times \sqrt{3} \times \sqrt{2}}{2} $$

Now we can multiply the terms in the numerator:

$$ \frac{4 \times \sqrt{3} \times \sqrt{2}}{2} = \frac{4 \times \sqrt{6}}{2} $$

Finally, we simplify by dividing 4 by 2:

$$ \frac{4 \times \sqrt{6}}{2} = 2 \times \sqrt{6} $$

So $4 \times \sqrt{3} \div \sqrt{2}$ simplifies to $2 \times \sqrt{6}$.