Question

Evaluate √50625 and hence find the value of √5.0625 + √506.25.​

Answer 1

Answer:

24.75

Step-by-step explanation:

50625 = 3 x 3 x 3 x 3 x 5 x 5 x 5 x 5 = $3^{4} * 5^{4}$

=>√50625 =  $\sqrt{3^{4}*5^{4} }$ = 3²*5² = 15² = 225

therefore,

√5.0625 = $\sqrt{\frac{50625}{10000} }$ = $\frac{\sqrt{50625} }{\sqrt{10000} }$ = 225/100 = 2.25  -------------(1)

√506.25 = $\sqrt{\frac{50625}{100} }$ = $\frac{\sqrt{50625} }{\sqrt{100} }$ = 225/10 = 22.5 ------------------(2)

=> √5.0625 + √506.25 = 2.25 + 2.5   ( by (1) & )2) )

=> √5.0625 + √506.25 = 2.25 + 22.5 = 24.75