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

Question

Solve:

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

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

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

$\sqrt{4}=2$

$4^2=4\times4=16$

$5^2=5\times5=25$

$\sqrt{1}=1$

Now we rearrange the exercise accordingly:

$2\times16-25\times1$

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:

$(2\times16)-(25\times1)=32-25=7$