**Algebra Practice Questions for Grade 10 :**

Here we are going to see, some practice questions on from different topics of algebra.

**Question 1 :**

Find the square root of 289x^{4} −612x^{3} + 970x^{2} −684x + 361.

**Solution :**

**Question 2 :**

Solve √(y + 1) + √(2y −5) = 3

**Solution :**

**√(y + 1) + √(2y −5) = 3**

**√(y + 1) = 3 - ****√(2y −5)**

**Taking squares on both sides**

**[√(y + 1)] ^{2} = [3 - **

**(y + 1) = 9 - 6****√(2y −5) + (2y - 5)**

**y + 1 - 2y + 5 - 9 = ****- 6****√(2y −5)**

**- y - 3 ****= ****- 6****√(2y −5)**

**[- (y + 3)] ^{2 }**

**y ^{2} + 6y + 9 = 36(2y - 5) **

**y ^{2} + 6y - 72y + 9 + 180 = 0**

**y ^{2} - 66y + 189 = 0**

**(y - 63)(y - 3) = 0**

**y = 63 and y = 3**

**Question 3 :**

A boat takes 1.6 hours longer to go 36 kms up a river than down the river. If the speed of the water current is 4 km per hr, what is the speed of the boat in still water?

**Solution :**

Distance covered = 36 kms

Let "x" be the speed of boat

Let "y" be the speed of stream = 4 km

Speed of down stream = x + y = x + 4

Speed of up stream = x - y = x - 4

Time taken = 1.6 hours

Time = Distance / Speed

Time taken for upstream = 36/(x - 4) ---(1)

Time taken for downstream = 36/(x + 4) ---(2)

(1) + (2)

36[1/(x - 4) - 1/(x + 4)] = 1.6

x + 4 - x + 4/(x + 4)(x - 4) = 1.6/36

8/(x^{2} - 16) = 16/360

2880 = 16(x^{2} - 16)

2880 = 16x^{2} - 256

2880 + 256 = 16x^{2}

16x^{2 }= 3136

x^{2 }= 196

x = 14

Hence the speed of the boat is 14 km/hr.

**Question 4 :**

Is it possible to design a rectangular park of perimeter 320 m and area 4800 m^{2} ? If so find its length and breadth.

**Solution :**

Perimeter of the rectangular park = 320 m

Area of park = 4800

2(l + b) = 320

l + b = 160---(1)

l x b = 4800

l = 4800/b

By applying the value of l in (1), we get

(4800/b) + b = 160

(4800 + b^{2})/b = 160

4800 + b^{2} = 160b

b^{2} - 160b + 4800 = 0

(b - 120)(b - 40) = 0

b = 120 and b = 40

If b = 120, then l = 4800/120 = 40

If b = 40, then l = 4800/40 = 120

Hence the required measurements are 120 m and 40 m.

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