Operations with Radical Expressions
1. Simplify the expression: 4 times Start Root 18 End Root plus 5 times Start Root 32 End Root (1 point)
45 times the square root of 2
32 times the square root of 2👈
116 times the square root of 2
9 times the square root of 50
2. Simplify the expression: 7 times Start Root 5 End Root minus 3 times Start Root 80 End Root (1 point)
negative 5 times the square root of 5👈
negative 4 times the square root of 75
–5
4 times the square root of negative 75
3. Simplify the expression: Start Root 21 End Root times Left Parenthesis Start Root 3 End Root plus Start Root 14 End Root Right Parenthesis. (1 point)
9 times Start Root 7 End Root minus 49 times Start Root 6 End Root
2 times Start Root 6 End Root plus Start Root 35 End Root
3 times Start Root 7 End Root plus 7 times Start Root 6 End Root👈
The square root of 375
4. Simplify by rationalizing the denominator: Start Fraction 4 over Start Root 10 End Root minus Start Root 6 End Root End Fraction (1 point)
Start Root 10 End Root plus Start Root 6 End Root👈
4
4 times Start Root 10 End Root plus 4 times Start Root 6 End Root
Start Fraction 4 times Start Root 10 End Root minus 4 times Start Root 6 End Root over 16 minus 2 times Start Root 15 End Root End Fraction
1)B
2)A
3)C
4)A
gave u a like bc its correct :D
To simplify the expression in question 1, we are given two numbers inside square roots: 18 and 32. We can simplify square roots by breaking down the number inside the square root into its prime factorization.
For the first number, 18, we can break it down as follows: 18 = 2 * 9 = 2 * 3 * 3 = 2 * 3^2.
For the second number, 32, we can break it down as follows: 32 = 2 * 16 = 2 * 2 * 8 = 2 * 2 * 2 * 4 = 2 * 2 * 2 * 2 * 2 = 2^5.
Now, let's simplify the expression using these prime factorizations:
4 * √18 + 5 * √32 = 4 * √(2 * 3^2) + 5 * √(2^5)
= 4 * √2 * √(3^2) + 5 * √(2^5)
= 4 * √2 * 3 + 5 * √(2^2 * 2^2 * 2)
= 12√2 + 20√2
= 32√2.
So, the simplified expression is 32 times the square root of 2.
Therefore, the correct answer is 32 times the square root of 2 (option B).