How do you simplify 2 square root 216 + 4square root 150?

First rewrite the terms in radicals as:

Next, use this rule for radicals to simplify the radicals:

Now, we can factor our the common term to complete the simplification:

To simplify the expression 2√216 + 4√150, we can first find the prime factorization of the numbers inside the square roots.

The prime factorization of 216 is 2^3 × 3^3, and the prime factorization of 150 is 2 × 3 × 5^2.

Now, we can simplify the expression by taking out any perfect square factors from under the square roots.

For 216, we can take out 2^2 × 3^2, which leaves us with 2√6.

For 150, we can take out 2 × 5, which leaves us with 2√6.

Therefore, the simplified expression becomes 2√6 + 4√6.

Since both terms have the same square root, we can combine them by adding the coefficients.

2√6 + 4√6 = 6√6.

So, the simplified form of 2√216 + 4√150 is 6√6.

To simplify ( 2\sqrt{216} + 4\sqrt{150} ), first, find the prime factorization of the numbers inside the square roots. Then, simplify each square root term separately and combine like terms.

(216 = 2^3 \times 3^3)
(150 = 2 \times 3 \times 5^2)

(2\sqrt{216} + 4\sqrt{150} = 2 \times 6 \sqrt{6} + 4 \times 5 \sqrt{6})
(= 12\sqrt{6} + 20\sqrt{6})
(= (12 + 20)\sqrt{6})
(= 32\sqrt{6})

So, (2\sqrt{216} + 4\sqrt{150}) simplifies to (32\sqrt{6}).