Find the Product of sqrt(3) and 2sqrt(5) 2. Write the expansion of 2x(sqrt(3) − 4sqrt(2)) 3. find the Sun of…

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Find the Product of sqrt(3) and 2sqrt(5) 2. Write the expansion of 2x(sqrt(3) − 4sqrt(2)) 3. find the Sun of (3sqrt(5)−4sqrt(2)) and (3sqrt(5)+5sqrt(2)) 4. Simplify sqrt(240)

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Here are the solutions to your homework problems:

Find the Product of $4\sqrt{3}$ and $2\sqrt{5}$

Multiply the coefficients and the terms under the square root.
$(4\sqrt{3}) \times (2\sqrt{5}) = (4 \times 2) \times (\sqrt{3} \times \sqrt{5})$
Simplify the product.
$8 \times \sqrt{3 \times 5} = 8\sqrt{15}$
The product is $\boxed{8\sqrt{15}}$ .
1. Write the expansion of $2x(4\sqrt{3} - \sqrt{2})$
Distribute $2x$ to each term inside the parenthesis.
$2x(4\sqrt{3} - \sqrt{2}) = (2x \times 4\sqrt{3}) - (2x \times \sqrt{2})$
Simplify each product.
$8x\sqrt{3} - 2x\sqrt{2}$
The expansion is $\boxed{8x\sqrt{3} - 2x\sqrt{2}}$ .
1. Find the Sum of $(3\sqrt{5} - 4\sqrt{2})$ and $(3\sqrt{5} + 5\sqrt{2})$
Combine the two expressions by addition.
$(3\sqrt{5} - 4\sqrt{2}) + (3\sqrt{5} + 5\sqrt{2})$
Group like terms (terms with $\sqrt{5}$ and terms with $\sqrt{2}$ ).
$(3\sqrt{5} + 3\sqrt{5}) + (-4\sqrt{2} + 5\sqrt{2})$
Add the coefficients of the like terms.
$(3+3)\sqrt{5} + (-4+5)\sqrt{2} = 6\sqrt{5} + 1\sqrt{2}$
The sum is $\boxed{6\sqrt{5} + \sqrt{2}}$ .
1. Simplify $\sqrt{240}$
Find the largest perfect square factor of 240.
The factors of 240 are $1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240$ .
The perfect square factors are $1, 4, 16$ . The largest is 16.
So, $240 = 16 \times 15$ .
Rewrite the square root using the factors.
$\sqrt{240} = \sqrt{16 \times 15}$
Simplify the perfect square factor.
$\sqrt{16} \times \sqrt{15} = 4\sqrt{15}$
The simplified form is $\boxed{4\sqrt{15}}$ .

Find the Product of sqrt(3) and 2sqrt(5) 2. Write the expansion of 2x(sqrt(3) - 4sqrt(2)) 3. find the Sun of (3sqrt(5)-4sqrt(2)) and (3sqrt(5)+5sqrt(2)) 4. Simplify sqrt(240)

Step-by-step solution

Multiply the coefficients and the terms under the square root.

Simplify the product.

Distribute $2x$ to each term inside the parenthesis.

Simplify each product.

Combine the two expressions by addition.

Group like terms (terms with $\sqrt{5}$ and terms with $\sqrt{2}$ ).

Add the coefficients of the like terms.

Find the largest perfect square factor of 240.

Rewrite the square root using the factors.

Simplify the perfect square factor.

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