Answer:
[tex]5\sqrt{7} [/tex]
Step-by-step explanation:
[tex]\frac{30\sqrt{14} }{6\sqrt{2} } [/tex]
Cancel out 6 in both numerator and denominator.
[tex]\frac{5\sqrt{14} }{\sqrt{2} } [/tex] Rationalize the denominator of [tex]\frac{5\sqrt{14} }{\sqrt{2} } [/tex] by multiplying the numerator and denominator by [tex]\sqrt{2} [/tex].
[tex]\frac{5\sqrt{14}\sqrt{2} }{(\sqrt{2})^{2} } [/tex]
The square of [tex]\sqrt{2} [/tex] is 2
Factor 14=2 × 7. Rewrite the square root of the product [tex]\sqrt{2x7} [/tex] as the product of square roots [tex]\sqrt{2}\sqrt{7} [/tex].
[tex]\frac{5\sqrt{2}\sqrt{7}\sqrt{2} }{2} [/tex]
Multiply [tex]\sqrt{2} [/tex] and [tex]\sqrt{2} [/tex] to get 2.
[tex]\frac{5x2\sqrt{7} }{2} [/tex]
Cancel out 2 and 2.
[tex]5\sqrt{7} [/tex]
Hope it helps and have a great day! =D
