Question

What must be subtracted from 3$\sqrt[2]{245}$ + 2$\sqrt[2]{275}$ + $\sqrt[2]{2245}$ to get $\sqrt[2]{25}$

• A. 27$\sqrt[2]{25}$
• B. 25$\sqrt[2]{25}$
• C. 22$\sqrt[2]{25}$
• D. 29$\sqrt[2]{25}$

Answer 1

The correct option is B

25$\sqrt[2]{25}$

let the number to be subtracted be X

Then 3$\sqrt[2]{245}$ + 2$\sqrt[2]{2125}$ + $\sqrt[2]{2245}$ - X = $\sqrt[2]{25}$

which implies X = 3$\sqrt[2]{245}$ + 2$\sqrt[2]{2125}$ + $\sqrt[2]{2245}$ - $\sqrt[2]{25}$

X = 3$\sqrt[2]{2\left(9\right)\left(5\right)}$ + 2$\sqrt[2]{2\left(25\right)\left(5\right)}$ + $\sqrt[2]{2\left(49\right)\left(5\right)}$ - $\sqrt[2]{25}$

X = 3$\times$3$\sqrt[2]{25}$ + 2$\times$5$\sqrt[2]{25}$ + 7$\sqrt[2]{25}$ - $\sqrt[2]{25}$

X = 9$\sqrt[2]{25}$ + 10$\sqrt[2]{25}$ + 7$\sqrt[2]{25}$ - $\sqrt[2]{25}$

X = 26$\sqrt[2]{25}$ - $\sqrt[2]{25}$

X = 25$\sqrt[2]{25}$