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math problem without calculator?
how do i solve this problem without a calculator???
my teacher said I should start by using Difference of two squares a^2-b^2=(a+b)(a-b)on 103*105then I think it should be (104+1)(104-1)??. But I dont know how im going to solve this without a calculator :( can someone show me step by step. Because I want to learn. Thank you.
2 Answers
- PuzzlingLv 74 months agoFavorite Answer
For the innermost square root:
1 + 103 * 105
= 1 + (104 - 1)(104 + 1)
= 1 + 104² - 1
= 104²
That's all with a square root symbol, so:
√(104²) = 104
Now notice a pattern? The next level is:
1 + 102 * 104
= 1 + (103 - 1)(103 + 1)
= 1 + 103² - 1
= 103²
Again, that's under a square root so it simplifies to:
√(103²) = 103
If we continue the pattern we end up with the last square root having:
1 + 100 * 102
= 1 + (101 - 1)(101 + 1)
= 1 + 101² - 1
= 101²
Apply the square root and you have:
√(101²) = 101
Answer:
101
- KrishnamurthyLv 74 months ago
(((sqrt(1) + 100) (sqrt(1) + 101)) (sqrt(1) + 102)) sqrt(1 + 103×105)
= 110355024
