Question

select the correct answer.

what is this expression in simplified form?

\\2y^2\sqrt{15} + 5y\sqrt{15} - 3y^2\sqrt{60} + 7y\\

• \\(-4y^2\sqrt{15} + 12y\sqrt{15}\\)
• \\(2y^2\sqrt{15} + 5y\sqrt{15} - 3y^2\sqrt{60} + 7y\\)
• \\(y\sqrt{15} + 7y\\)
• \\(-4y^2\sqrt{15} + 5y\sqrt{15} + 7y\\)

Explanation:

⚡ Using what you learned: Simplifying Radical Expressions

Step 1: Simplify the radical term

Simplify the radical \(\sqrt{60}\) by factoring out the largest perfect square:

$$ \sqrt{60} = \sqrt{4 \times 15} = 2\sqrt{15} $$

Substitute this back into the term \(-3y^2\sqrt{60}\):

$$ -3y^2\sqrt{60} = -3y^2(2\sqrt{15}) = -6y^2\sqrt{15} $$

Step 2: Rewrite the expression

Substitute the simplified term back into the original expression:

$$ 2y^2\sqrt{15} + 5y\sqrt{15} - 6y^2\sqrt{15} + 7y $$

Step 3: Combine like terms

Group and combine the terms containing \(y^2\sqrt{15}\):

$$ (2y^2\sqrt{15} - 6y^2\sqrt{15}) + 5y\sqrt{15} + 7y $$

$$ -4y^2\sqrt{15} + 5y\sqrt{15} + 7y $$

Answer:

\(-4y^2\sqrt{15} + 5y\sqrt{15} + 7y\) (the fourth option)