The first image is the one that I fixed

The second image is my mistake

My mistake of the week was in the Pythagorean theorem question in page 32. At first, they gave us a right triangle with a hypotenuse of 19 cm and another length of 5 cm. After that they asked us to find the length of XY. We need to find it in a entire radical, mixed radical and the decimal to the nearest hundredth.

First step: c2=a2+b2

Second step: 192=52+XY2

Third step: 361=25+XY2

Forth step: XY2=361−25=336

Fifth step: XY=radical336

it was correct for now but when it got to the ​mixed radical I got confused and I made a mistake.

Now I need to turn the entire radical: radical 336 to mixed radical as what the question wants from us.

when we want to turn the entire radical to the mixed radical, we need to find the two perfect numbers or perfect squares and turn them into the simplest number for example the perfect square was: 4, 9, 16, 25, 36, 49, 64, 81, 100…

Than we would start dividing 336 into the perfect square from the smallest to largest, And also, 336 is a even number so it should be divided by even perfect square.

336÷4=84

336÷16=21, it would not ger simplest as this

16 would go outside of the radical and 21 would stay because it can’t get simpler than this.

The answer would be 4√21.

My mistake was that I started to divide 336 with 2 which it made me so confused and lost. I did this

336÷2=168

168÷2=84

84÷2=42

42÷2=21

I got so confused and I didn’t know what to do after. Later I found out that I should just divide the 336 with perfect squares to find the best number.

Overall

Mixed radical: 4√21

Entire radical: √336

A decimal to the nearest hundred: 18.33

Another example;

Hypotenuse 13 cm, leg 7 cm.

c2=132−72

c2=169−49

c2=120

120 is dividable with 2

√4×√30=√120

4 would go outside the radical and 30 stay inside

Mixed radical= 2√30

A decimal to the nearest hundred=10.95 cm

Entire radical= √120

My pattern : 0 pattern is just the red shape, 1st pattern has add tow small green triangle to it and  2rd pattern has added tow green triangle so the pattern goas like 2+2+2. 

N/P

0/0

1/2

2/4

3/6

p= 2n+0
The 15th pattern is 2×15=30

30+0=30

15th=30

What is the 10th figure look like?

2×10=20+0=20

What is the 5th figure look like?

2×5=10+0=10

Simplify evaluate powers in parentheses and brackets.

• 1. in step one we simplify the first numbers and power of to brackets or parentheses. for example: (*2²*+3)+(*4⁶*-6)
• 2. we (+,×,÷,-) the numbers in the prantheses or brackets. for example:(*2+3*)+(*4+7*)
• 3. we simplify the whole prantheses or brackets powers. for example =(2⁴+4)*³*+(5⁶+6⁷)*⁸*
• 4. we simplify the powers. *12⁶*

5. we get the answer. 49+49= 98