Subtract simplify by collecting like radical terms

6square root symbol 75 -7square root symbol 3

I cant figure out how to square 75?

sqrt(75)=sqrt(25)sqrt(3)

which simplifies to 5 times sqrt(3)
so 6x5xsqrt(3)= 30 sqrt(3)

Simplify.

5 times the square root of 75

To simplify the expression involving the square roots, we need to first evaluate the square roots of the numbers under the radical symbols.

To find the square root of 75, we need to prime factorize the number:

75 = 3 * 5 * 5

Now, group the prime factors in pairs, taking one factor from each pair and writing it outside the radical symbol:

√(3 * 5 * 5)

Since we have one factor left over (3), it cannot be paired, so it remains under the square root:

5√3

Now we can substitute the simplified form of the first term back into the original expression:

6√75 - 7√3

becomes

6 * 5√3 - 7√3

= 30√3 - 7√3

Now, we have like terms with the same radical, so we can combine them:

= (30 - 7)√3

= 23√3

Therefore, the simplified expression is 23√3.