# Quick way to simplify (12(sqrt(2) + 17)

• bigevil
In summary, the conversation discusses difficulties with arriving at precise answers in a textbook, specifically in regards to a particular problem involving factorization and simplification. The person suggests a method of using the property of perfect squares to arrive at the answer more quickly.
bigevil

## Homework Statement

This isn't really a problem at all. Have been working on some problems in Mary L Boas' textbook with some difficulty, but I have managed to solve the majority of the questions eventually. However, I've been stumped at how to arrive at the precise answers quoted in the book.

For instance, one of the answers is $$\frac{1}{32} (51\sqrt{2} - ln (1 + \sqrt{2})$$. But due to the method of arriving at the answer, my answer was $$\frac{1}{32}(51\sqrt{2}) - \frac{1}{128}(ln (17 + 2\sqrt{2})$$ which is equivalent (12 root 2 + 17 = (1 + rt 2)^4, after working backwards). But I'm wondering if there's actually a way to factorise or simplify my original (12 rt 2 + 17) quickly without working backwards.

bigevil said:

## Homework Statement

This isn't really a problem at all. Have been working on some problems in Mary L Boas' textbook with some difficulty, but I have managed to solve the majority of the questions eventually. However, I've been stumped at how to arrive at the precise answers quoted in the book.

For instance, one of the answers is $$\frac{1}{32} (51\sqrt{2} - ln (1 + \sqrt{2})$$. But due to the method of arriving at the answer, my answer was $$\frac{1}{32}(51\sqrt{2}) - \frac{1}{128}(ln (17 + 2\sqrt{2})$$ which is equivalent (12 root 2 + 17 = (1 + rt 2)^4, after working backwards). But I'm wondering if there's actually a way to factorise or simplify my original (12 rt 2 + 17) quickly without working backwards.

Hi bigevil!

(have a square-root: √ )

This is a bit of a hindsight way too …

you could have noticed that (17 + 12√2)(17 - 12√2) = 289 - 288 = 1,

so any factor was going to have the same property …

like 1 ± √2 and 3 ± 4√2

Thanks tim! That's pretty clever...

## 1. How do you simplify the expression (12(sqrt(2) + 17)?

To simplify this expression, you can start by distributing the 12 to both terms inside the parentheses. This will give you 12(sqrt(2)) + 12(17). From there, you can simplify the first term to 12(sqrt(2)) = 12√2. The second term, 12(17) can be simplified to 204. Therefore, the simplified expression is 12√2 + 204.

## 2. Can this expression be simplified further?

No, this expression cannot be simplified any further. It is in its simplest form.

## 3. How did you simplify the expression?

I simplified the expression by using the distributive property to multiply 12 to both terms inside the parentheses. Then, I simplified the individual terms by evaluating any square roots or multiplying any numbers.

## 4. Is there a faster way to simplify this expression?

Yes, there is a faster way to simplify this expression. Instead of using the distributive property, you can use the distributive law of square roots, which states that √(a + b) = √a + √b. In this case, you can rewrite the expression as 12√(2 + 17), which simplifies to 12√19.

## 5. Can this expression be written in a different form?

Yes, this expression can be written in a different form. It can also be written as 12√2 + 12√17, which is equivalent to the simplified form of 12√2 + 204.

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