Question 80

$$\sqrt[4]{17 + 12\sqrt{2}} =$$

Solution

$$\sqrt[4]{17+12\sqrt{2}}=\sqrt[4]{9+8+12\sqrt{2}}$$

$$=\sqrt[4]{3^2+\left(2\sqrt{2}\right)^2+2\left(3\right)\left(2\sqrt{2}\right)}$$

$$=\sqrt[4]{\left(3+2\sqrt{2}\right)^2}$$

$$=\sqrt{3+2\sqrt{2}}$$

$$=\sqrt{1+2+2\sqrt{2}}$$

$$=\sqrt{1^2+\left(\sqrt{2}\right)^2+2\left(1\right)\left(\sqrt{2}\right)}$$

$$=\sqrt{\left(1+\sqrt{2}\right)^2}$$

$$=1+\sqrt{2}$$

Hence, the correct answer is Option B

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