Question

Determine o valor do "X".

a)√175=X√7

b)√92=2√X

c)√X=9√7

Answer 1

a) $\sqrt{175}=x\sqrt{7}$

$x=\dfrac{\sqrt{175}}{\sqrt{7}}\\ \\ x=\sqrt{\dfrac{175}{7}}\\ \\ x=\sqrt{25}\\ \\ x=5$


b) $\sqrt{92}=2\sqrt{x}$

$\left(\sqrt{92} \right )^{2}=\left(2\sqrt{x} \right )^{2}\\ \\ 92=2^{2}\cdot \left(\sqrt{x} \right )^{2}\\ \\ 92=4\cdot x\\ \\ x=\dfrac{92}{4}\\ \\ x=23$


c) $\sqrt{x}=9\sqrt{7}$

$\left(\sqrt{x} \right )^{2}=\left(9\sqrt{7} \right )^{2}\\ \\ x=9^{2}\cdot \left(\sqrt{7} \right )^{2}\\ \\ x=81\cdot 7\\ \\ x=567$