Add simplify by collecting like radical terms if possible
3�ã45+4�ã180
3√45 + 4√180
= 3√9√5 + 4√√36√5
= 9√5 + 24√5
= 33√5
To add and simplify the expression 3√45 + 4√180, you first need to determine if there are any like radical terms that can be combined.
Step 1: Simplify the radicals individually.
√45 can be simplified by finding its prime factors. The prime factorization of 45 is 3 × 3 × 5. Since there are two 3s, you can take one of them out of the radical sign. That leaves you with √45 = 3√5.
√180 can also be simplified using prime factorization. The prime factorization of 180 is 2 × 2 × 3 × 3 × 5. Similarly, there are two 2s and two 3s, so you can take one of each out of the radical sign. This simplifies √180 to 2√45.
Step 2: Write the simplified radicals.
After simplifying the radicals individually, the expression becomes 3√5 + 4(2√45).
Step 3: Rearrange the expression.
To collect like terms, rearrange the terms in the expression. Write the radicals with similar terms next to each other.
The new expression is 3√5 + 8√45.
Step 4: Combine the coefficients of the like terms.
Now, you can add the coefficients of the like terms, which are 3 and 8. The resulting expression is 11√45 + 3√5.
So, the simplified form of 3√45 + 4√180 is 11√45 + 3√5.