$$[(3024 \div 189)^{\frac{1}{2}} + (684 \div 19)^{2}] = (?)^{2}+ 459$$

Solution

Expression : $$[(3024 \div 189)^{\frac{1}{2}} + (684 \div 19)^{2}] = (?)^{2}+ 459$$

=> $$(\frac{3024}{189})^{\frac{1}{2}} + (\frac{684}{19})^2 = (x)^2 + 459$$

=> $$(16){\frac{1}{2}} + (36)^2 = (x)^2 + 459$$

=> $$4 + 1296 = (x)^2 + 459$$

=> $$(x)^2 = 1300 - 459 = 841$$

=> $$x = \sqrt{841} = \pm 29$$

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