Calculate the Difference: √400 - √225 Step by Step

400225= \sqrt{400}-\sqrt{225}=

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Step-by-step video solution

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00:00 Solve
00:03 Square root of any number (X) squared, root cancels square
00:07 We break down 400 to 20 squared
00:15 We break down 225 to 15 squared
00:19 We'll use this formula in our exercise
00:22 Root and square cancel out
00:28 Let's calculate and solve
00:34 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

400225= \sqrt{400}-\sqrt{225}=

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Find 400\sqrt{400}.
  • Step 2: Find 225\sqrt{225}.
  • Step 3: Subtract 225\sqrt{225} from 400\sqrt{400}.

Now, let's work through each step:
Step 1: Calculate 400\sqrt{400}. Since 400=202400 = 20^2, it follows that 400=20\sqrt{400} = 20.

Step 2: Calculate 225\sqrt{225}. Since 225=152225 = 15^2, it follows that 225=15\sqrt{225} = 15.

Step 3: Subtract 225\sqrt{225} from 400\sqrt{400}:

2015=520 - 15 = 5.

Therefore, the solution to the problem is 5\boxed{5}.

3

Final Answer

5

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\( \sqrt{100}= \)

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