Question

\\(\sqrt{700} = \\) simplify and remove all perfect squares

question 8

simplify: \\(\sqrt3{1296}\\)

Explanation:

Factor the radicand for the first expression

Find the largest perfect square factor of \(700\).
Using the Simplifying Radicals knowledge point:

$$ 700 = 100 \times 7 $$

Simplify the square root

Apply the product property of radicals.
Using the Simplifying Radicals knowledge point:

$$ \sqrt{700} = \sqrt{100 \times 7} = \sqrt{100} \times \sqrt{7} = 10\sqrt{7} $$

Factor the radicand for the second expression

Find the prime factorization of \(1296\).
Using the Simplifying Radicals knowledge point:

$$ 1296 = 2^4 \times 3^4 = 16 \times 81 $$

Simplify the cube root

Group factors into perfect cubes to simplify.
Using the Simplifying Radicals knowledge point:

$$ \sqrt[3]{1296} = \sqrt[3]{2^3 \times 2 \times 3^3 \times 3} = \sqrt[3]{8 \times 27 \times 6} = \sqrt[3]{216 \times 6} = 6\sqrt[3]{6} $$

Answer:

Question 1

\(\sqrt{700} = \) <blank>\(10\sqrt{7}\)</blank>

Question 2

Simplify: \(\sqrt[3]{1296} = \) <blank>\(6\sqrt[3]{6}\)</blank>