Solve: Square Root of 4 Times 4 Squared Minus 5 Squared

Solve:

442521 \sqrt{4}\cdot4^2-5^2\cdot\sqrt{1}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:05 Always calculate roots and exponents first
00:08 An exponent is actually the number multiplied by itself as many times as the power
00:11 Break down each exponent into multiplications and solve
00:24 The root of 1 is always equal to 1
00:29 Always solve multiplication and division before addition and subtraction
00:36 That's the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve:

442521 \sqrt{4}\cdot4^2-5^2\cdot\sqrt{1}

2

Step-by-step solution

We simplify each term according to the order from left to right:

4=2 \sqrt{4}=2

42=4×4=16 4^2=4\times4=16

52=5×5=25 5^2=5\times5=25

1=1 \sqrt{1}=1

Now we rearrange the exercise accordingly:

2×1625×1 2\times16-25\times1

Since there are two multiplication operations in the exercise, according to the order of operations we start with them and then subtract.

We put the two multiplication exercises in parentheses to avoid confusion during the solution, and solve from left to right:

(2×16)(25×1)=3225=7 (2\times16)-(25\times1)=32-25=7

3

Final Answer

7

Practice Quiz

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What is the result of the following equation?

\( 36-4\div2 \)

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