Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify
(2√5+3√7)^2
. Show your work. Justify each step.
i Just need someone to explain to me how to solve it because idk how to solve it, i just need help, dont be rude
Can someone please help me!
To simplify the given expression, we will use the distributive property and the rule of squaring a binomial.
Step 1: Start by expanding the square of the binomial using the distributive property:
(2√5 + 3√7)^2 = (2√5 + 3√7)(2√5 + 3√7)
Step 2: Apply the distributive property:
= (2√5)(2√5) + (2√5)(3√7) + (3√7)(2√5) + (3√7)(3√7)
Step 3: Simplify by multiplying the terms:
= 4(√5)(√5) + 6(√5)(√7) + 6(√7)(√5) + 9(√7)(√7)
Step 4: Use the product rule of radicals to simplify the square roots:
= 4(√(5 × 5)) + 6(√(5 × 7)) + 6(√(7 × 5)) + 9(√(7 × 7))
Step 5: Simplify the expressions inside the square roots:
= 4√25 + 6√35 + 6√35 + 9√49
Step 6: Simplify the square roots:
= 4(5) + 6√35 + 6√35 + 9(7)
Step 7: Perform the multiplications and combine like terms:
= 20 + 12√35 + 12√35 + 63
Step 8: Further simplify by combining like terms:
= 83 + 24√35
Therefore, the simplified form of (2√5 + 3√7)^2 is 83 + 24√35.