Question

plz answer correctly​

Answer 1

Question :

Find the value of x in

$\sf{\dfrac{x}{\sqrt{72}} = \dfrac{\sqrt{288}}{x}}$

Answer :-

• The value of x is ±12.

To Find :-

• The value of x

★ Solution:

$\sf{ \longrightarrow \: \dfrac{x}{\sqrt{72}} = \dfrac{\sqrt{288}}{x}}$

By cross-multiplication,

$\sf{ \longrightarrow \: x \times x = \sqrt{288} \times \sqrt{72}}$

By simplifying,

$\sf{ \longrightarrow \: {x}^{2} = \sqrt{288} \times \sqrt{72}}$

$\sf{ \longrightarrow \: {x}^{2} = \sqrt{288 \times 72}}$

$\sf{ \longrightarrow \: {x}^{2} = \sqrt{20736}}$

$\sf{ \longrightarrow \: {x}^{2} = \sqrt{144 \times 144}}$

$\sf{ \longrightarrow \: {x}^{2} = 144}$

$\sf{ \longrightarrow \: {x}^{2} = 12 \times 12}$

$\longrightarrow \: \sf{x = \pm \: 12} \: \: \: \: \: \bigstar$

Hence, The value of x is ±12.

V E R I F I C A T I O N :-

• $\sf{ \dfrac{x}{\sqrt{72}} = \dfrac{\sqrt{288}}{x}}$

By putting the value of x,

$\sf{ \longrightarrow \: \dfrac{12}{\sqrt{72}} = \dfrac{\sqrt{288}}{12}}$

By cross-multiplication,

$\sf{ \longrightarrow \: 12 \times 12 = \sqrt{288} \times \sqrt{72}}$

$\sf{ \longrightarrow \: 144 = \sqrt{288 \times 72}}$

$\sf{ \longrightarrow \: 144 = 144}$

L.H.S = R.H.S

Hence, Verified!