Simplifying expressions containing radicals and fractions relies on correctly applying order of operations rules and properties of radicals. Combining radical and fraction operations introduces additional steps compared to expressions with just radicals or just fractions. In this post, we’ll evaluate the expression √2/2, explaining how to simplify radicals with fractions systematically. We’ll also explore strategies for manipulating more complex radical and fractional expressions.

## What is the √2 divided by 2?

*The square root of 2 divided by 2, written as √2/2, simplifies to (1/2)√2. It is an irrational number approximately equal to 0.7071067811865476 when rounded to several decimal places. This value is commonly encountered in trigonometry as the sine or cosine of 45 degrees in a right triangle with equal legs.*

Here’s a table that shows the value of √2 divided by 2:

Expression | Value |
---|---|

√2 / 2 | Approximately 0.7071 |

So, √2 divided by 2 is approximately equal to 0.7071 when rounded to four decimal places.

Reviewing Radicals and Fractions First, let’s review some key concepts and properties:

- Radicals indicate taking the nth root of a number. Example: √9 = 3.
- Fractions represent division of numerator by denominator. Example: 1/2 = 0.5.
- When simplifying, perform radical operations before fraction operations.
- Radicals can be written as fractional exponents. Example: √x = x^(1/2).

Keeping these rules in mind, let’s evaluate our expression √2/2.

## Evaluating √2/2 Step-by-Step

Following proper order:

- Evaluate radical first: √2/2
- Write radical as fractional exponent: (2^(1/2))/2
- Simplify fraction: 2^(1/2) / 2^1
- Subtract exponents: 2^(1/2 – 1)
- Simplify: 2^(-1/2)

Therefore, the simplified form is 2^(-1/2).

## Explanation of the Steps

- Radicals come before fractions in PEMDAS order.
- Fractional exponents allow combining and simplifying.
- Numerator and denominator exponents can be subtracted.
- Leaving the result as a fractional exponent is the simplified form.

## Strategies for Simplifying Radicals and Fractions

Some helpful strategies:

- Memorize order of operations PEMDAS.
- Write radicals as fractional exponents to enable simplification.
- Break each step into chunks using parentheses if needed.
- Double check by evaluating result with calculator.
- Practice essential rules until they become intuitive.

## FAQs

**How do you solve root 2 divided by 2?** To solve √2 divided by 2, you simply divide √2 by 2: √2 / 2 = (1/2)√2

**What is the value of 2√2 in numbers?** The value of 2√2 is approximately 2.8284.

**How do you simplify square root 2 divided by 2?** I already answered this in the first question. To simplify √2 divided by 2, it is (1/2)√2.

**How do you simplify √2?** √2 is already in its simplest form, but you can approximate it as approximately 1.4142.

**Can square root of 2 be divided by 2?** Yes, as mentioned earlier, you can divide the square root of 2 by 2, which gives you (1/2)√2.

**How does root 2 by 2 become 1 by root 2?** Root 2 divided by 2 does not become 1 by root 2. It is equal to (1/2)√2. If you want to represent it as a reciprocal, you could write it as 1/(√2).

**What’s 2 million look like?** 2 million can be written numerically as 2,000,000.

**How do you write one million?** One million is written numerically as 1,000,000.

**How many 7 digit numbers are there in all?** There are 9,000,000 seven-digit numbers in total, ranging from 1,000,000 to 9,999,999.

**Is the square root of 2 divided by 2 irrational?** Yes, the square root of 2 divided by 2 is irrational. The square root of 2 is itself an irrational number, and dividing an irrational number by a rational number (2 in this case) still results in an irrational number.

**How do you turn √2 into a fraction?** You can write √2 as a fraction by expressing it as (√2/1) and rationalizing the denominator: (√2/1) * (√2/√2) = (2/2) = 1 So, √2 as a fraction is 1/√2.

**How do you solve √2 by long division method?** To calculate √2 by long division method, you would perform division similar to long division, but since √2 is an irrational number, it has a non-repeating, non-terminating decimal expansion. The long division method will keep producing more and more decimal places without repeating.

**What is 2 times root 2?** 2 times √2 is equal to 2√2.

**How do you simplify a root?** To simplify a square root, you look for perfect squares that can be factored out from under the radical sign. For example, √18 can be simplified as √(9 * 2), and then you can take the square root of 9, which is 3, and write it as 3√2.

**How to solve √8?** To simplify √8, you can factor it as √(4 * 2) and then take the square root of 4, which is 2, and write it as 2√2. So, √8 is equal to 2√2.

## Conclusion

In this post, we showed the step-by-step work to simplify √2/2 to an equivalent fractional exponent form 2^(-1/2) by methodically applying PEMDAS order and properties of exponents and radicals. Taking the time to explain the logic reinforces good practices for manipulating complex symbolic expressions.

Building fluency with radicals, fractions, and exponents is key scaffolding for higher level math and science coursework. Patience and perseverance working through many examples develops skills, pattern recognition, and conceptual understanding.

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