Solving 7th Grade Mathematics Page 32 from Volume 1 of the Knowledge Connection textbook provides detailed guidance on solving exercises 2.6 to 2.12 in the lesson on Irrational Numbers, Square Roots in a very specific and detailed manner. If you are facing difficulties, unsure how to solve, you can refer to and compare with the solutions.
Refer to other Mathematics solving materials:
- See the complete set of solutions for 7th Grade Mathematics from the Knowledge Connection textbook
- Solving 7th Grade Mathematics Page 47 from Volume 1 of the Kite book - Exercise 3. Absolute Value of a Real Number
- Solving 7th Grade Mathematics Page 45 from Volume 1 of the Bright Horizon book - Final exercises of chapter 2
Solving 7th Grade Mathematics Page 32 from Volume 1 of the Knowledge Connection textbook
Irrational Numbers. Mathematical Square Roots
1. Solve Exercise 2.6 Page 32 SGK Math Grade 7
2. Solve Exercise 2.7 Page 32 SGK Math Grade 7
Problem Statement: From the numbers that are squares of the first 12 natural numbers, find the square roots of the following:
a) 9; b) 16;
c) 81; d) 121.
Step-by-step solution:
Answer:
3. Solution for Exercise 2.8 on Page 32 of 7th Grade Mathematics Textbook
Problem Statement: When finding the square root of a natural number, we usually decompose the number into prime factors. For example:
Calculate the square root of 129,600.
Step-by-step solution:
Decompose 129,600 into prime factors, then express it in the form of a2.
Answer:
4. Solution for Exercise 2.9 on Page 32 of 7th Grade Mathematics Textbook
Problem Statement: Calculate the length of the side of the square with an area equal to:
a) 81 square decimeters; b) 3,600 square meters; c) 1 hectare
Guidance:
Apply the method of finding the square root of a number:
Pay attention to the units.
Answer:
5. Solve Exercise 2.10 Page 32 of 7th Grade Mathematics Textbook
Problem Statement: Use a handheld calculator to find the square root of the following numbers and round the results to an accuracy of 0.005.
a) 3; b) 41; c) 2 021
Guidance:
* Use a calculator to find the square root.
* Round according to the decimal rounding rules.
- For rounding the digit place:
+ Keep unchanged if the digit immediately to the right is less than 5;
+ Increase by 1 unit if the digit immediately to the right is greater than or equal to 5.
- For rounding the digit place after the decimal:
+ Remove if in the decimal part;
+ Replace with 0 digits if in the integer part.
Answer:
Round the results to an accuracy of 0.005, which means rounding to the hundredths place.
We have:
6. Solve Exercise 2.11 Page 32 SGK Mathematics Grade 7
Problem Statement: Given that the square of the length of the diagonal of a rectangle is equal to the sum of the squares of its two sides. A rectangle has a length of 8 dm and a width of 5 dm. What is the length of the diagonal of the rectangle in decimeters (round the result to the nearest tenth)?
Step-by-step solution:
Step 1: Calculate the sum of the squares of the lengths of the two sides of the rectangle.
Step 2: Find the square root of the sum obtained using a handheld calculator.
Step 3: Round the result to the nearest tenth.
7. Solve Exercise 2.12 Page 32 SGK Mathematics Grade 7
Problem Statement: To pave a square-shaped piece of land with an area of 100 square meters, how many square tiles with a side length of 50 cm are needed (assuming negligible gaps between tiles)?
Step 1: Find the area of 1 tile. Convert all measurements to the same unit.
Step 2: Number of tiles = land area : tile area.
Answer:
Area of 1 tile: 502 = 2500 (cm2). Convert 2500 cm2 = 0.25 m2. Number of tiles needed: 100 : 0.25 = 400 (tiles).
The area of 1 tile is:
502 = 2500 (cm2)
Convert 2500 cm2 = 0.25 m2.
Number of tiles needed:
100 ÷ 0.25 = 400 (tiles).
Here is the solution to Grade 7 Mathematics page 32 Volume 1 of the Knowledge Connection textbook. We hope that through this effective Mathematics learning material, students have been able to do exercises efficiently.
Next Exercise:
- Solve Grade 7 Mathematics page 36 Volume 1 of the Knowledge Connection textbook - Exercise 7: Set of Real Numbers
- Solve Grade 7 Mathematics page 38 Volume 1 of the Knowledge Connection textbook - Concentration exercises on page 38
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