Simplify √75 + √24 · √2 − √12

Sure, let's simplify the expression step by step:

√75 + √24 · √2 − √12

First, we simplify the square roots:

√75 = √(253) = 5√3 √24 = √(46) = 2√6 √2 = √2 √12 = √(4*3) = 2√3

So, the expression becomes:

5√3 + 2√6 * √2 - 2√3

Next, we simplify the multiplication:

2√6 * √2 = 2√12 = 2*2√3 = 4√3

So, the expression becomes:

5√3 + 4√3 - 2√3

Finally, we combine like terms:

(5√3 + 4√3 - 2√3) = 7√3

So, √75 + √24 · √2 − √12 simplifies to 7√3.