How do you solve #3 sqrt18 - 2sqrt2#?

Question

Eva Abramson · Accepted Answer

#7sqrt(2)# #18=2xx9 = 2xx3^2# Write as:#" "3sqrt(2xx3^2)-2sqrt(2)# #=>9sqrt(2)-2sqrt(2)# #= 7sqrt(2)#

Eva Abramson · Answer

#color(green)(7sqrt(2))# #sqrt(18)=sqrt(3^2 * 2) = 3sqrt(2)# So #color(white)("XXX")3sqrt(18)-2sqrt(2)# #color(white)("XXX")=(3 * 3) sqrt(2)-2sqrt(2)# #color(white)("XXX")=9sqrt(2)-2sqrt(2)# #color(white)("XXX")=7sqrt(2)#

Eva Adamson · Answer

undefined To solve 3√18 - 2√2, we can simplify each square root separately and then subtract the results.

First, let's simplify √18. We can break down 18 into its prime factors: 18 = 2 × 3 × 3. Since there is no perfect square factor, we cannot simplify it further. Therefore, √18 remains as √18.

Next, let's simplify √2. Since 2 is a prime number, √2 cannot be simplified further. Therefore, √2 remains as √2.

Now, we substitute the simplified square roots back into the original expression: 3√18 - 2√2 = 3(√18) - 2(√2).

Substituting the values we found earlier, we have: 3(√18) - 2(√2) = 3(√(2 × 3 × 3)) - 2(√2).

Simplifying further, we get: 3(√(2 × 3 × 3)) - 2(√2) = 3(√(2) × √(3) × √(3)) - 2(√2).

Now, we can simplify the expression inside the parentheses: 3(√(2) × √(3) × √(3)) - 2(√2) = 3(√2 × 3) - 2(√2).

Multiplying the coefficients, we have: 3(√2 × 3) - 2(√2) = 9√2 - 2√2.

Finally, we can combine like terms: 9√2 - 2√2 = (9 - 2)√2 = 7√2.

Therefore, the simplified form of 3√18 - 2√2 is 7√2.