In Exercises 29–36, simplify and write the result in standard ...

Question

In Exercises 29–36, simplify and write the result in standard form.

√3² − 4 ⋅ 2 ⋅ 5

Accepted Answer

Welcome back, everyone simplify the following expression and express the answer in standard form, square root of four squared minus four, multiplied by one multiplied by 10. We are given four answer choices. A two I square root of three B two, I square root of six C four I and D two I. So let's begin simplifying it. So we are evaluating for squared minus four multiplied by one multiplied by 10 based on the order of operations, we first will have to deal with exponents. So four squared is 16 and then we are subtracting a product. So now let's evaluate the product four multiplied by one is just four and four multiplied by 10 gives us 40. So we are subtracting 40 from 16. And then we simply have to take the square root of the result, right? Let's rewrite the square root sign 16 minus 40 gives us negative 24. Now, if we're taking square root of a negative number, we're going to get an imaginary number. Specifically, we're getting a complex number, right? And let's recall that square root of negative one is equal to I, what we can do is basically rewrite the given expression as square root of 24 multiplied by square root of negative one, right. This is based on the property of radicals. We can essentially split our product into a product of two individual roots. Let's begin simplifying score of 24. And we want to isolate the perfect square from 24. Let's recall that 24 can be rewritten as four multiplied by six, which is just two squared multiplied by six, right. So we get square root of two squared multiplied by squared of six and then multiplied by square root of negative one, starting with the first term square root of two squared is basically two. Now square root of six is just square root of six. We cannot simplify it further and then square root of negative one by definition is simply I, when we combine those, we end up with two square root of sex I which corresponds to the intero B. Thank you for watching.

In Exercises 29–36, simplify and write the result in standard form.

√3² − 4 ⋅ 2 ⋅ 5

Key Concepts

Square Roots

Order of Operations

Standard Form

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